数据库系统基础教程第二章答案
大数据库系统基础教程(第二版)课后习题问题详解
Database Systems: The CompleteBookSolutions for Chapter 2Solutions for Section 2.1Exercise 2.1.1The E/R Diagram.Exercise 2.1.8(a)The E/R DiagramKobvxybzSolutions for Section 2.2Exercise 2.2.1The Addresses entity set is nothing but a single address, so we would prefer to make address an attribute of Customers. Were the bank to record several addresses for a customer, then it might make sense to have an Addresses entity set and make Lives-at a many-many relationship.The Acct-Sets entity set is useless. Each customer has a unique account set containing his or her accounts. However, relating customers directly to their accounts in a many-many relationship conveys the same information and eliminates the account-set concept altogether.Solutions for Section 2.3Exercise 2.3.1(a)Keys ssNo and number are appropriate for Customers and Accounts, respectively.Also,we think it does not make sense for an account to be related to zero customers, so we should round the edge connecting Owns to Customers. It does not seem inappropriate to have a customer with 0 accounts; they might be a borrower, for example, so we put no constraint on the connection from Owns to Accounts. Here is the The E/R Diagram，showing underlined keys and the numerocity constraint.Exercise 2.3.2(b)If R is many-one from E1 to E2, then two tuples (e1,e2) and (f1,f2) of the relationship set for R must be the same if they agree on the key attributes for E1. To see why, surely e1 and f1 are the same. Because R is many-one from E1 to E2, e2 and f2 must also be the same. Thus, the pairs are the same.Solutions for Section 2.4Exercise 2.4.1Here is the The E/R Diagram.We have omitted attributes other than our choice for the key attributes of Students and Courses. Also omitted are names for the relationships. Attribute grade is not part of the key for Enrollments. The key for Enrollements is studID from Students and dept and number from Courses.Exercise 2.4.4bHere is the The E/R Diagram Again, we have omitted relationship names and attributes other than our choice for the key attributes. The key for Leagues is its own name; this entity set is not weak. The key for Teams is its own name plus the name of theleague of which the team is a part, e.g., (Rangers, MLB) or (Rangers, NHL). The key for Players consists of the player's number and the key for the team on which he or she plays. Since the latter key is itself a pair consisting of team and league names, the key for players is the triple (number, teamName, leagueName). e.g., Jeff Garcia is (5, 49ers, NFL).Database Systems: The CompleteBookSolutions for Chapter 3Solutions for Section 3.1Exercise 3.1.2(a)We can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36.Solutions for Section 3.2Exercise 3.2.1Customers(ssNo, name, address, phone)Flights(number, day, aircraft)Bookings(ssNo, number, day, row, seat)Being a weak entity set, Bookings' relation has the keys for Customers and Flights and Bookings' own attributes.Notice that the relations obtained from the toCust and toFlt relationships are unnecessary. They are:toCust(ssNo, ssNo1, number, day)toFlt(ssNo, number, day, number1, day1)That is, for toCust, the key of Customers is paired with the key for Bookings. Since both include ssNo, this attribute is repeated with two different names, ssNo and ssNo1. A similar situation exists for toFlt.Exercise 3.2.3Ships(name, yearLaunched)SisterOf(name, sisterName)Solutions for Section 3.3Exercise 3.3.1Since Courses is weak, its key is number and the name of its department. We do not have a relation for GivenBy. In part (a), there is a relation for Courses and a relation for LabCourses that has only the key and the computer-allocation attribute. It looks like:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, allocation)For part (b), LabCourses gets all the attributes of Courses, as:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, room, allocation)And for (c), Courses and LabCourses are combined, as:Depts(name, chair)Courses(number, deptName, room, allocation)Exercise 3.3.4(a)There is one relation for each entity set, so the number of relations is e. The relation for the root entity set has a attributes, while the other relations, which must include the key attributes, have a+k attributes.Solutions for Section 3.4Exercise 3.4.2Surely ID is a key by itself. However, we think that the attributes x, y, and z together form another key. The reason is that at no time can two molecules occupy the same point.Exercise 3.4.4The key attributes are indicated by capitalization in the schema below:Customers(SSNO, name, address, phone)Flights(NUMBER, DAY, aircraft)Bookings(SSNO, NUMBER, DAY, row, seat)Exercise 3.4.6(a)The superkeys are any subset that contains A1. Thus, there are 2^{n-1} such subsets, since each of the n-1 attributes A2 through An may independently be chosen in or out.Solutions for Section 3.5Exercise 3.5.1(a)We could try inference rules to deduce new dependencies until we are satisfied we have them all. A more systematic way is to consider the closures of all 15 nonempty sets of attributes.For the single attributes we have A+ = A, B+ = B, C+ = ACD, and D+ = AD. Thus, the only new dependency we get with a single attribute on the left is C->A.Now consider pairs of attributes:AB+ = ABCD, so we get new dependency AB->D. AC+ = ACD, and AC->D is nontrivial. AD+ = AD, so nothing new. BC+ = ABCD, so we get BC->A, and BC->D. BD+ = ABCD, giving us BD->A and BD->C. CD+ = ACD, giving CD->A.For the triples of attributes, ACD+ = ACD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC->D, ABD->C, and BCD->A.Since ABCD+ = ABCD, we get no new dependencies.The collection of 11 new dependencies mentioned above is: C->A, AB->D, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.Exercise 3.5.1(b)From the analysis of closures above, we find that AB, BC, and BD are keys. All other sets either do not have ABCD as the closure or contain one of these three sets.Exercise 3.5.1(c)The superkeys are all those that contain one of those three keys. That is, a superkey that is not a key must contain B and more than one of A, C, and D. Thus, the (proper) superkeys are ABC, ABD, BCD, and ABCD.Exercise 3.5.3(a)We must compute the closure of A1A2...AnC. Since A1A2...An->B is a dependency, surely B is in this set, proving A1A2...AnC->B.Exercise 3.5.4(a)Consider the relationThis relation satisfies A->B but does not satisfy B->A.Exercise 3.5.8(a)If all sets of attributes are closed, then there cannot be any nontrivial functional dependencies. For suppose A1A2...An->B is a nontrivial dependency. Then A1A2...An+ contains B and thus A1A2...An is not closed.Exercise 3.5.10(a)We need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:A+ = AB+ = BC+ = ACEAB+ = ABCDEAC+ = ACEBC+ = ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC are: C->A and AB->C. Note that BC->A is true, but follows logically from C->A, and therefore may be omitted from our list.Solutions for Section 3.6Exercise 3.6.1(a)In the solution to Exercise 3.5.1 we found that there are 14 nontrivial dependencies, including the three given ones and 11 derived dependencies. These are: C->A, C->D, D->A, AB->D, AB-> C, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.We also learned that the three keys were AB, BC, and BD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. These are: C->A, C->D, D->A, AC->D, and CD->A.One choice is to decompose using C->D. That gives us ABC and CD as decomposed relations. CD is surely in BCNF, since any two-attribute relation is. ABC is not in BCNF, since AB and BC are its only keys, but C->A is a dependency that holds in ABCD and therefore holds in ABC. We must further decompose ABC into AC and BC. Thus, the three relations of the decomposition are AC, BC, and CD.Since all attributes are in at least one key of ABCD, that relation is already in 3NF, and no decomposition is necessary.Exercise 3.6.1(b)(Revised 1/19/02) The only key is AB. Thus, B->C and B->D are both BCNF violations. The derived FD's BD->C and BC->D are also BCNF violations. However, any other nontrivial, derived FD will have A and B on the left, and therefore will contain a key.One possible BCNF decomposition is AB and BCD. It is obtained starting with any of the four violations mentioned above. AB is the only key for AB, and B is the only key for BCD.Since there is only one key for ABCD, the 3NF violations are the same, and so is the decomposition.Solutions for Section 3.7Exercise 3.7.1Since A->->B, and all the tuples have the same value for attribute A, we can pair the B-value from any tuple with the value of the remaining attribute C from any othertuple. Thus, we know that R must have at least the nine tuples of the form (a,b,c), where b is any of b1, b2, or b3, and c is any of c1, c2, or c3. That is, we can derive, using the definition of a multivalued dependency, that each of the tuples (a,b1,c2), (a,b1,c3), (a,b2,c1), (a,b2,c3), (a,b3,c1), and (a,b3,c2) are also in R.Exercise 3.7.2(a)First, people have unique Social Security numbers and unique birthdates. Thus, we expect the functional dependencies ssNo->name and ssNo->birthdate hold. The same applies to children, so we expect childSSNo->childname and childSSNo->childBirthdate. Finally, an automobile has a unique brand, so we expect autoSerialNo->autoMake.There are two multivalued dependencies that do not follow from these functional dependencies. First, the information about one child of a person is independent of other information about that person. That is, if a person with social security number s has a tuple with cn,cs,cb, then if there is any other tuple t for the same person, there will also be another tuple that agrees with t except that it has cn,cs,cb in its components for the child name, Social Security number, and birthdate. That is the multivalued dependencyssNo->->childSSNo childName childBirthdateSimilarly, an automobile serial number and make are independent of any of the other attributes, so we expect the multivalued dependencyssNo->->autoSerialNo autoMakeThe dependencies are summarized below:ssNo -> name birthdatechildSSNo -> childName childBirthdateautoSerialNo -> autoMakessNo ->-> childSSNo childName childBirthdatessNo ->-> autoSerialNo autoMakeExercise 3.7.2(b)We suggest the relation schemas{ssNo, name, birthdate}{ssNo, childSSNo}{childSSNo, childName childBirthdate}{ssNo, autoSerialNo}{autoSerialNo, autoMake}An initial decomposition based on the two multivalued dependencies would give us {ssNo, name, birthDate}{ssNo, childSSNo, childName, childBirthdate}{ssNo, autoSerialNo, autoMake}Functional dependencies force us to decompose the second and third of these.Exercise 3.7.3(a)Since there are no functional dependencies, the only key is all four attributes,ABCD. Thus, each of the nontrvial multivalued dependencies A->->B and A->->C violate 4NF. We must separate out the attributes of these dependencies, first decomposing into AB and ACD, and then decomposing the latter into AC and AD because A->->C is still a 4NF violation for ACD. The final set of relations are AB, AC, and AD.Exercise 3.7.7(a)Let W be the set of attributes not in X, Y, or Z. Consider two tuples xyzw and xy'z'w' in the relation R in question. Because X ->-> Y, we can swap the y's, so xy'zw and xyz'w' are in R. Because X ->-> Z, we can take the pair of tuples xyzw and xyz'w' and swap Z's to get xyz'w and xyzw'. Similarly, we can take the pair xy'z'w' and xy'zw and swap Z's to get xy'zw' and xy'z'w.In conclusion, we started with tuples xyzw and xy'z'w' and showed that xyzw' and xy'z'w must also be in the relation. That is exactly the statement of the MVD X ->-> Y-union-Z. Note that the above statements all make sense even if there are attributes in common among X, Y, and Z.Exercise 3.7.8(a)Consider a relation R with schema ABCD and the instance with four tuples abcd, abcd', ab'c'd, and ab'c'd'. This instance satisfies the MVD A ->-> BC. However, it does not satisfy A ->-> B. For example, if it did satisfy A ->-> B, then because the instance contains the tuples abcd and ab'c'd, we would expect it to contain abc'd and ab'cd, neither of which is in the instance.Database Systems: The Complete Array BookSolutions for Chapter 4Solutions for Section 4.2Exercise 4.2.1class Customer {attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account {attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Exercise 4.2.4class Person {attribute string name;relationship Person motherOfinverse Person::childrenOfFemalerelationship Person fatherOfinverse Person::childrenOfMalerelationship Set<Person> childreninverse Person::parentsOfrelationship Set<Person> childrenOfFemaleinverse Person::motherOfrelationship Set<Person> childrenOfMaleinverse Person::fatherOfrelationship Set<Person> parentsOfinverse Person::children}Notice that there are six different relationships here. For example, the inverse of the relationship that connects a person to their (unique) mother is a relationship that connects a mother (i.e., a female person) to the set of her children. That relationship, which we call childrenOfFemale, is different from the children relationship, which connects anyone -- male or female -- to their children.Exercise 4.2.7A relationship R is its own inverse if and only if for every pair (a,b) in R, the pair (b,a) is also in R. In the terminology of set theory, the relation R is ``symmetric.''Solutions for Section 4.3Exercise 4.3.1We think that Social Security number should me the key for Customer, and account number should be the key for Account. Here is the ODL solution with key and extent declarations.class Customer(extent Customers key ssNo){attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account(extent Accounts key number){attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Solutions for Section 4.4Exercise 4.4.1(a)Since the relationship between customers and accounts is many-many, we should create a separate relation from that relationship-pair.Customers(ssNo, name, address, phone)Accounts(number, type, balance)CustAcct(ssNo, number)Exercise 4.4.1(d)Ther is only one attribute, but three pairs of relationships from Person to itself. Since motherOf and fatherOf are many-one, we can store their inverses in the relation for Person. That is, for each person, childrenOfMale and childrenOfFemale will indicate that persons's father and mother. The children relationship is many-many, and requires its own relation. This relation actually turns out to be redundant, in the sense that its tuples can be deduced from the relationships stored with Person. The schema:Persons(name, childrenOfFemale, childrenOfMale)Parent-Child(parent, child)Exercise 4.4.4You get a schema like:Studios(name, address, ownedMovie)Since name -> address is the only FD, the key is {name, ownedMovie}, and the FD has a left side that is not a superkey.Exercise 4.4.5(a,b,c)(a) Struct Card { string rank, string suit };(b) class Hand {attribute Set theHand;};For part (c) we have:Hands(handId, rank, suit)Notice that the class Hand has no key, so we need to create one: handID. Each hand has, in the relation Hands, one tuple for each card in the hand.Exercise 4.4.5(e)Struct PlayerHand { string Player, Hand theHand };class Deal {attribute Set theDeal;}Alternatively, PlayerHand can be defined directly within the declaration of attribute theDeal.Exercise 4.4.5(h)Since keys for Hand and Deal are lacking, a mechanical way to design the database schema is to have one relation connecting deals and player-hand pairs, and another to specify the contents of hands. That is:Deals(dealID, player, handID)Hands(handID, rank, suit)However, if we think about it, we can get rid of handID and connect the deal and the player directly to the player's cards, as:Deals(dealID, player, rank, suit)Exercise 4.4.5(i)First, card is really a pair consisting of a suit and a rank, so we need two attributes in a relation schema to represent cards. However, much more important is the fact that the proposed schema does not distinguish which card is in which hand. Thus, we need another attribute that indicates which hand within the deal a card belongs to, something like:Deals(dealID, handID, rank, suit)Exercise 4.4.6(c)Attribute b is really a bag of (f,g) pairs. Thus, associated with each a-value will be zero or more (f,g) pairs, each of which can occur several times. We shall use an attribute count to indicate the number of occurrences, although if relations allow duplicate tuples we could simply allow duplicate (a,f,g) triples in the relation. The proposed schema is:C(a, f, g, count)Solutions for Section 4.5Exercise 4.5.1(b)Studios(name, address, movies{(title, year, inColor, length,stars{(name, address, birthdate)})})Since the information about a star is repeated once for each of their movies, there is redundancy. To eliminate it, we have to use a separate relation for stars anduse pointers from studios. That is:Stars(name, address, birthdate)Studios(name, address, movies{(title, year, inColor, length,stars{*Stars})})Since each movie is owned by one studio, the information about a movie appears in only one tuple of Studios, and there is no redundancy.Exercise 4.5.2Customers(name, address, phone, ssNo, accts{*Accounts})Accounts(number, type, balance, owners{*Customers})Solutions for Section 4.6Exercise 4.6.1(a)We need to add new nodes labeled George Lucas and Gary Kurtz. Then, from the node sw (which represents the movie Star Wars), we add arcs to these two new nodes, labeled directedBy and producedBy, respectively.Exercise 4.6.2Create nodes for each account and each customer. From each customer node is an arc to a node representing the attributes of the customer, e.g., an arc labeled name to the customer's name. Likewise, there is an arc from each account node to each attribute of that account, e.g., an arc labeled balance to the value of the balance. To represent ownership of accounts by customers, we place an arc labeled owns from each customer node to the node of each account that customer holds (possibly jointly). Also, we place an arc labeled ownedBy from each account node to the customer node for each owner of that account.Exercise 4.6.5In the semistructured model, nodes represent data elements, i.e., entities rather than entity sets. In the E/R model, nodes of all types represent schema elements, and the data is not represented at all.Solutions for Section 4.7Exercise 4.7.1(a)<STARS-MOVIES><STAR starId = "cf" starredIn = "sw, esb, rj"><NAME>Carrie Fisher</NAME><ADDRESS><STREET>123 Maple St.</STREET><CITY>Hollywood</CITY></ADDRESS><ADDRESS><STREET>5 Locust Ln.</STREET><CITY>Malibu</CITY></ADDRESS></STAR><STAR starId = "mh" starredIn = "sw, esb, rj"><NAME>Mark Hamill</NAME><ADDRESS><STREET>456 Oak Rd.<STREET><CITY>Brentwood</CITY></ADDRESS></STAR><STAR starId = "hf" starredIn = "sw, esb, rj, wit"> <NAME>Harrison Ford</NAME><ADDRESS><STREET>whatever</STREET><CITY>whatever</CITY></ADDRESS></STAR><MOVIE movieId = "sw" starsOf = "cf, mh"><TITLE>Star Wars</TITLE><YEAR>1977</YEAR></MOVIE><MOVIE movieId = "esb" starsOf = "cf, mh"><TITLE>Empire Strikes Back</TITLE><YEAR>1980</YEAR></MOVIE><MOVIE movieId = "rj" starsOf = "cf, mh"><TITLE>Return of the Jedi</TITLE><YEAR>1983</YEAR></MOVIE><MOVIE movieID = "wit" starsOf = "hf"><TITLE>Witness</TITLE><YEAR>1985</YEAR></MOVIE></STARS-MOVIES>Exercise 4.7.2<!DOCTYPE Bank [<!ELEMENT BANK (CUSTOMER* ACCOUNT*)><!ELEMENT CUSTOMER (NAME, ADDRESS, PHONE, SSNO)> <!ATTLIST CUSTOMERcustId IDowns IDREFS><!ELEMENT NAME (#PCDATA)><!ELEMENT ADDRESS (#PCDATA)><!ELEMENT PHONE (#PCDATA)><!ELEMENT SSNO (#PCDATA)><!ELEMENT ACCOUNT (NUMBER, TYPE, BALANCE)><!ATTLIST ACCOUNTacctId IDownedBy IDREFS><!ELEMENT NUMBER (#PCDATA)><!ELEMENT TYPE (#PCDATA)><!ELEMENT BALANCE (#PCDATA)>]>Database Systems: The Complete Array BookSolutions for Chapter 5Solutions for Section 5.2Exercise 5.2.1(a)PI_model( SIGMA_{speed >= 1000} ) (PC)Exercise 5.2.1(f)The trick is to theta-join PC with itself on the condition that the hard disk sizes are equal. That gives us tuples that have two PC model numbers with the same value of hd. However, these two PC's could in fact be the same, so we must also require in the theta-join that the model numbers be unequal. Finally, we want the hard disk sizes, so we project onto hd. The expression is easiest to see if we write it using some temporary values. We start by renaming PC twice so we can talk about two occurrences of the same attributes.R1 = RHO_{PC1} (PC)R2 = RHO_{PC2} (PC)R3 = R1 JOIN_{PC1.hd = PC2.hd AND PC1.model <> PC2.model} R2R4 = PI_{PC1.hd} (R3)Exercise 5.2.1(h)First, we find R1, the model-speed pairs from both PC and Laptop. Then, we find from R1 those computers that are ``fast,'' at least 133Mh. At the same time, we join R1 with Product to connect model numbers to their manufacturers and we project out the speed to get R2. Then we join R2 with itself (after renaming) to find pairs of different models by the same maker. Finally, we get our answer, R5, by projecting onto one of the maker attributes. A sequence of steps giving the desired expression is:R1 = PI_{model,speed} (PC) UNION PI_{model,speed} (Laptop)R2 = PI_{maker,model} (SIGMA_{speed>=700} (R1) JOIN Product)R3 = RHO_{T(maker2, model2)} (R2)R4 = R2 JOIN_{maker = maker2 AND model <> model2} (R3)R5 = PI_{maker} (R4)Exercise 5.2.2Here are figures for the expression trees of Exercise 5.2.1 Part (a)Part (f)Part (h). Note that the third figure is not really a tree, since it uses a common subexpression. We could duplicate the nodes to make it a tree, but using common subexpressions is a valuable form of query optimization. One of the benefits one gets from constructing ``trees'' for queries is the ability to combine nodes that represent common subexpressions.Exercise 5.2.7The relation that results from the natural join has only one attribute from each pair of equated attributes. The theta-join has attributes for both, and their columns are identical.Exercise 5.2.9(a)If all the tuples of R and S are different, then the union has n+m tuples, and this number is the maximum possible.The minimum number of tuples that can appear in the result occurs if every tuple of one relation also appears in the other. Surely the union has at least as many tuples as the larger of R and that is, max(n,m) tuples. However, it is possible for every tuple of the smaller to appear in the other, so it is possible that there are as few as max(n,m) tuples in the union.Exercise 5.2.10In the following we use the name of a relation both as its instance (set of tuples) and as its schema (set of attributes). The context determines uniquely which is meant.PI_R(R JOIN S) Note, however, that this expression works only for sets; it does not preserve the multipicity of tuples in R. The next two expressions work for bags.R JOIN DELTA(PI_{R INTERSECT S}(S)) In this expression, each projection of a tuple from S onto the attributes that are also in R appears exactly once in the second argument of the join, so it preserves multiplicity of tuples in R, except for those that do not join with S, which disappear. The DELTA operator removes duplicates, as described in Section 5.4. R - [R - PI_R(R JOIN S)] Here, the strategy is to find the dangling tuples of R and remove them.Solutions for Section 5.3Exercise 5.3.1As a bag, the value is {700, 1500, 866, 866, 1000, 1300, 1400, 700, 1200, 750, 1100, 350, 733}. The order is unimportant, of course. The average is 959.As a set, the value is {700, 1500, 866, 1000, 1300, 1400, 1200, 750, 1100, 350, 733}, and the average is 967. H3>Exercise 5.3.4(a)As sets, an element x is in the left-side expression(R UNION S) UNION Tif and only if it is in at least one of R, S, and T. Likewise, it is in the right-side expressionR UNION (S UNION T)under exactly the same conditions. Thus, the two expressions have exactly the same members, and the sets are equal.As bags, an element x is in the left-side expression as many times as the sum of the number of times it is in R, S, and T. The same holds for the right side. Thus, as bags the expressions also have the same value.Exercise 5.3.4(h)As sets, element x is in the left sideR UNION (S INTERSECT T)if and only if x is either in R or in both S and T. Element x is in the right side(R UNION S) INTERSECT (R UNION T)if and only if it is in both R UNION S and R UNION T. If x is in R, then it is in both unions. If x is in both S and T, then it is in both union. However, if x is neither in R nor in both of S and T, then it cannot be in both unions. For example, suppose x is not in R and not in S. Then x is not in R UNION S. Thus, the statement of when x is in the right side is exactly the same as when it is in the left side: x is either in R or in both of S and T.Now, consider the expression for bags. Element x is in the left side the sum of the number of times it is in R plus the smaller of the number of times x is in S and the number of times x is in T. Likewise, the number of times x is in the right side is the smaller ofThe sum of the number of times x is in R and in S.The sum of the number of times x is in R and in T.A moment's reflection tells us that this minimum is the sum of the number of times x is in R plus the smaller of the number of times x is in S and in T, exactly as for the left side.Exercise 5.3.5(a)For sets, we observe that element x is in the left side(R INTERSECT S) - Tif and only if it is in both R and S and not in T. The same holds for the right sideR INTERSECT (S-T)so as sets, the equivalence holds.Now suppose we have bags. Let R = {x}, S = {x,x}, and T = {x}. Then R INTERSECT S = {x}, and the left side is {x}-{x}, or EMPTYSET. However, on the right, S-T = {x}, so the right side is {x} INTERSECT {x}, which is {x}.Solutions for Section 5.4Exercise 5.4.1(a){(1,0,1), (5,4,9), (1,0,1), (6,4,16), (7,9,16)}.Exercise 5.4.1(c)。
数据库系统基础学习知识原理与设计(第2版)课后习题集详细规范标准答案
数据库系统原理与设计习题集第一章绪论一、选择题1. DBS是采用了数据库技术的计算机系统，DBS是一个集合体，包含数据库、计算机硬件、软件和（）。
A. 系统分析员B. 程序员C. 数据库管理员D. 操作员2. 数据库（DB），数据库系统（DBS）和数据库管理系统（DBMS）之间的关系是（）。
A. DBS包括DB和DBMSB. DBMS包括DB和DBSC. DB包括DBS和DBMSD. DBS就是DB，也就是DBMS3. 下面列出的数据库管理技术发展的三个阶段中，没有专门的软件对数据进行管理的是（）。
I．人工管理阶段II．文件系统阶段III．数据库阶段A. I 和IIB. 只有IIC. II 和IIID. 只有I4. 下列四项中，不属于数据库系统特点的是（）。
A. 数据共享B. 数据完整性C. 数据冗余度高D. 数据独立性高5. 数据库系统的数据独立性体现在（）。
A.不会因为数据的变化而影响到应用程序B.不会因为系统数据存储结构与数据逻辑结构的变化而影响应用程序C.不会因为存储策略的变化而影响存储结构D.不会因为某些存储结构的变化而影响其他的存储结构6. 描述数据库全体数据的全局逻辑结构和特性的是（）。
A. 模式B. 内模式C. 外模式D. 用户模式7. 要保证数据库的数据独立性，需要修改的是（）。
A. 模式与外模式B. 模式与内模式C. 三层之间的两种映射D. 三层模式8. 要保证数据库的逻辑数据独立性，需要修改的是（）。
A. 模式与外模式的映射B. 模式与内模式之间的映射C. 模式D. 三层模式9. 用户或应用程序看到的那部分局部逻辑结构和特征的描述是（），它是模式的逻辑子集。
A.模式B. 物理模式C. 子模式D. 内模式10.下述（）不是DBA数据库管理员的职责。
A.完整性约束说明B. 定义数据库模式C.数据库安全D. 数据库管理系统设计选择题答案：(1) C (2) A (3) D (4) C (5) B(6) A (7) C (8) A (9) C (10) D二、简答题１．试述数据、数据库、数据库系统、数据库管理系统的概念。
数据库系统基础教程(第二版)课后习题答案
Database Systems: The Complete BookSolutions for Chapter 2Solutions for Section 2.1Exercise 2.1.1The E/R Diagram.Exercise 2.1.8(a)The E/R DiagramKobvxybzSolutions for Section 2.2Exercise 2.2.1The Addresses entity set is nothing but a single address, so we would prefer to make address an attribute of Customers. Were the bank to record several addresses for a customer, then it might make sense to have an Addresses entity set and make Lives-at a many-many relationship.The Acct-Sets entity set is useless. Each customer has a unique account set containing his or her accounts. However, relating customers directly to their accounts in a many-many relationship conveys the same information and eliminates the account-set concept altogether.Solutions for Section 2.3Exercise 2.3.1(a)Keys ssNo and number are appropriate for Customers and Accounts, respectively. Also, we think it does not make sense for an account to be related to zero customers, so we should round the edgeconnecting Owns to Customers. It does not seem inappropriate to have a customer with 0 accounts;they might be a borrower, for example, so we put no constraint on the connection from Owns to Accounts. Here is the The E/R Diagram，showing underlined keys and the numerocity constraint.Exercise 2.3.2(b)If R is many-one from E1 to E2, then two tuples (e1,e2) and (f1,f2) of the relationship set for R must be the same if they agree on the key attributes for E1. To see why, surely e1 and f1 are the same. Because R is many-one from E1 to E2, e2 and f2 must also be the same. Thus, the pairs are the same.Solutions for Section 2.4Exercise 2.4.1Here is the The E/R Diagram.We have omitted attributes other than our choice for the key attributes of Students and Courses. Also omitted are names for the relationships. Attribute grade is not part of the key for Enrollments. The key for Enrollements is studID from Students and dept and number from Courses.Exercise 2.4.4bHere is the The E/R Diagram Again, we have omitted relationship names and attributes other than our choice for the key attributes. The key for Leagues is its own name; this entity set is not weak. The key for Teams is its own name plus the name of the league of which the team is a part, e.g., (Rangers, MLB) or (Rangers, NHL). The key for Players consists of the player's number and the key for the team on which he or she plays. Since the latter key is itself a pair consisting of team and league names, the key for players is the triple (number, teamName, leagueName). e.g., JeffGarcia is (5, 49ers, NFL).Database Systems: The Complete BookSolutions for Chapter 3Solutions for Section 3.1Exercise 3.1.2(a)We can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36.Solutions for Section 3.2Exercise 3.2.1Customers(ssNo, name, address, phone)Flights(number, day, aircraft)Bookings(ssNo, number, day, row, seat)Being a weak entity set, Bookings' relation has the keys for Customers and Flights and Bookings' own attributes.Notice that the relations obtained from the toCust and toFlt relationships are unnecessary. They are:toCust(ssNo, ssNo1, number, day)toFlt(ssNo, number, day, number1, day1)That is, for toCust, the key of Customers is paired with the key for Bookings. Since both include ssNo, this attribute is repeated with two different names, ssNo and ssNo1. A similar situation exists for toFlt.Exercise 3.2.3Ships(name, yearLaunched)SisterOf(name, sisterName)Solutions for Section 3.3Exercise 3.3.1Since Courses is weak, its key is number and the name of its department. We do not havearelation for GivenBy. In part (a), there is a relation for Courses and a relation for LabCourses that has only the key and the computer-allocation attribute. It looks like:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, allocation)For part (b), LabCourses gets all the attributes of Courses, as:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, room, allocation)And for (c), Courses and LabCourses are combined, as:Depts(name, chair)Courses(number, deptName, room, allocation)Exercise 3.3.4(a)There is one relation for each entity set, so the number of relations is e. The relation for the root entity set has a attributes, while the other relations, which must include the key attributes, have a+k attributes.Solutions for Section 3.4Exercise 3.4.2Surely ID is a key by itself. However, we think that the attributes x, y, and z together form another key. The reason is that at no time can two molecules occupy the same point.Exercise 3.4.4The key attributes are indicated by capitalization in the schema below:Customers(SSNO, name, address, phone)Flights(NUMBER, DAY, aircraft)Bookings(SSNO, NUMBER, DAY, row, seat)Exercise 3.4.6(a)The superkeys are any subset that contains A1. Thus, there are 2^{n-1} such subsets, since each of the n-1 attributes A2 through An may independently be chosen in or out.Solutions for Section 3.5Exercise 3.5.1(a)We could try inference rules to deduce new dependencies until we are satisfied we have them all.A more systematic way is to consider the closures of all 15 nonempty sets of attributes.For the single attributes we have A+ = A, B+ = B, C+ = ACD, and D+ = AD. Thus, the only new dependency we get with a single attribute on the left is C->A.Now consider pairs of attributes:AB+ = ABCD, so we get new dependency AB->D. AC+ = ACD, and AC->D is nontrivial. AD+ = AD, so nothing new. BC+ = ABCD, so we get BC->A, and BC->D. BD+ = ABCD, giving usBD->A and BD->C. CD+ = ACD, giving CD->A.For the triples of attributes, ACD+ = ACD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC->D, ABD->C, and BCD->A.Since ABCD+ = ABCD, we get no new dependencies.The collection of 11 new dependencies mentioned above is: C->A, AB->D, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.Exercise 3.5.1(b)From the analysis of closures above, we find that AB, BC, and BD are keys. All other sets either do not have ABCD as the closure or contain one of these three sets.Exercise 3.5.1(c)The superkeys are all those that contain one of those three keys. That is, a superkey that is not a key must contain B and more than one of A, C, and D. Thus, the (proper) superkeys are ABC, ABD, BCD, and ABCD.Exercise 3.5.3(a)We must compute the closure of A1A2...AnC. Since A1A2...An->B is a dependency, surely B is in this set, proving A1A2...AnC->B.Exercise 3.5.4(a)Consider the relationThis relation satisfies A->B but does not satisfy B->A.Exercise 3.5.8(a)If all sets of attributes are closed, then there cannot be any nontrivial functional dependencies. For suppose A1A2...An->B is a nontrivial dependency. Then A1A2...An+ contains B and thus A1A2...An is not closed.Exercise 3.5.10(a)We need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets: A+ = AB+ = BC+ = ACEAB+ = ABCDEAC+ = ACEBC+ = ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC are: C->A and AB->C. Note that BC->A is true, but follows logically from C->A, and therefore may be omitted from our list.Solutions for Section 3.6Exercise 3.6.1(a)In the solution to Exercise 3.5.1 we found that there are 14 nontrivial dependencies, including the three given ones and 11 derived dependencies. These are: C->A, C->D, D->A, AB->D, AB-> C, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.We also learned that the three keys were AB, BC, and BD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. These are: C->A, C->D, D->A, AC->D, and CD->A.One choice is to decompose using C->D. That gives us ABC and CD as decomposed relations. CD is surely in BCNF, since any two-attribute relation is. ABC is not in BCNF, since AB and BC are its only keys, but C->A is a dependency that holds in ABCD and therefore holds in ABC. We must further decompose ABC into AC and BC. Thus, the three relations of the decomposition are AC, BC, and CD.Since all attributes are in at least one key of ABCD, that relation is already in 3NF, and no decomposition is necessary.Exercise 3.6.1(b)(Revised 1/19/02) The only key is AB. Thus, B->C and B->D are both BCNF violations. The derived FD's BD->C and BC->D are also BCNF violations. However, any other nontrivial, derived FD will have A and B on the left, and therefore will contain a key.One possible BCNF decomposition is AB and BCD. It is obtained starting with any of the four violations mentioned above. AB is the only key for AB, and B is the only key for BCD.Since there is only one key for ABCD, the 3NF violations are the same, and so is the decomposition.Solutions for Section 3.7Exercise 3.7.1Since A->->B, and all the tuples have the same value for attribute A, we can pair the B-value from any tuple with the value of the remaining attribute C from any other tuple. Thus, we know that R must have at least the nine tuples of the form (a,b,c), where b is any of b1, b2, or b3, and c is any of c1, c2, or c3. That is, we can derive, using the definition of a multivalued dependency, that each of the tuples (a,b1,c2), (a,b1,c3), (a,b2,c1), (a,b2,c3), (a,b3,c1), and (a,b3,c2) are also in R.Exercise 3.7.2(a)First, people have unique Social Security numbers and unique birthdates. Thus, we expect the functional dependencies ssNo->name and ssNo->birthdate hold. The same applies to children, so we expect childSSNo->childname and childSSNo->childBirthdate. Finally, an automobile has a unique brand, so we expect autoSerialNo->autoMake.There are two multivalued dependencies that do not follow from these functional dependencies. First, the information about one child of a person is independent of other information about that person. That is, if a person with social security number s has a tuple with cn,cs,cb, then if there isany other tuple t for the same person, there will also be another tuple that agrees with t except that it has cn,cs,cb in its components for the child name, Social Security number, and birthdate. That is the multivalued dependencyssNo->->childSSNo childName childBirthdateSimilarly, an automobile serial number and make are independent of any of the other attributes, so we expect the multivalued dependencyssNo->->autoSerialNo autoMakeThe dependencies are summarized below:ssNo -> name birthdatechildSSNo -> childName childBirthdateautoSerialNo -> autoMakessNo ->-> childSSNo childName childBirthdatessNo ->-> autoSerialNo autoMakeExercise 3.7.2(b)We suggest the relation schemas{ssNo, name, birthdate}{ssNo, childSSNo}{childSSNo, childName childBirthdate}{ssNo, autoSerialNo}{autoSerialNo, autoMake}An initial decomposition based on the two multivalued dependencies would give us {ssNo, name, birthDate}{ssNo, childSSNo, childName, childBirthdate}{ssNo, autoSerialNo, autoMake}Functional dependencies force us to decompose the second and third of these.Exercise 3.7.3(a)Since there are no functional dependencies, the only key is all four attributes, ABCD. Thus, each of the nontrvial multivalued dependencies A->->B and A->->C violate 4NF. We must separate out the attributes of these dependencies, first decomposing into AB and ACD, and then decomposing the latter into AC and AD because A->->C is still a 4NF violation for ACD. The final set of relations are AB, AC, and AD.Exercise 3.7.7(a)Let W be the set of attributes not in X, Y, or Z. Consider two tuples xyzw and xy'z'w' in the relation R in question. Because X ->-> Y, we can swap the y's, so xy'zw and xyz'w' are in R. Because X ->-> Z, we can take the pair of tuples xyzw and xyz'w' and swap Z's to get xyz'w and xyzw'. Similarly, we can take the pair xy'z'w' and xy'zw and swap Z's to get xy'zw' and xy'z'w.In conclusion, we started with tuples xyzw and xy'z'w' and showed that xyzw' and xy'z'w must also be in the relation. That is exactly the statement of the MVD X ->-> Y-union-Z. Note that the above statements all make sense even if there are attributes in common among X, Y, and Z.Exercise 3.7.8(a)Consider a relation R with schema ABCD and the instance with four tuples abcd, abcd', ab'c'd, and ab'c'd'. This instance satisfies the MVD A ->-> BC. However, it does not satisfy A ->-> B. For example, if it did satisfy A ->-> B, then because the instance contains the tuples abcd and ab'c'd, we would expect it to contain abc'd and ab'cd, neither of which is in the instance.Solutions for Chapter 4Solutions for Section 4.2Exercise 4.2.1class Customer {attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account {attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Exercise 4.2.4class Person {attribute string name;relationship Person motherOfinverse Person::childrenOfFemalerelationship Person fatherOfinverse Person::childrenOfMalerelationship Set<Person> childreninverse Person::parentsOfrelationship Set<Person> childrenOfFemaleinverse Person::motherOfrelationship Set<Person> childrenOfMaleinverse Person::fatherOfrelationship Set<Person> parentsOfinverse Person::children}Notice that there are six different relationships here. For example, the inverse of the relationship that connects a person to their (unique) mother is a relationship that connects a mother (i.e., a female person) to the set of her children. That relationship, which we call childrenOfFemale, is different from the children relationship, which connects anyone -- male or female -- to their children.Exercise 4.2.7A relationship R is its own inverse if and only if for every pair (a,b) in R, the pair (b,a) is also in R. In the terminology of set theory, the relation R is ``symmetric.''Solutions for Section 4.3Exercise 4.3.1We think that Social Security number should me the key for Customer, and account number should be the key for Account. Here is the ODL solution with key and extent declarations.class Customer(extent Customers key ssNo){attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account(extent Accounts key number){attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Solutions for Section 4.4Exercise 4.4.1(a)Since the relationship between customers and accounts is many-many, we should create a separate relation from that relationship-pair.Customers(ssNo, name, address, phone)Accounts(number, type, balance)CustAcct(ssNo, number)Exercise 4.4.1(d)Ther is only one attribute, but three pairs of relationships from Person to itself. Since motherOf and fatherOf are many-one, we can store their inverses in the relation for Person. That is, for each person, childrenOfMale and childrenOfFemale will indicate that persons's father and mother. The children relationship is many-many, and requires its own relation. This relation actually turns out to be redundant, in the sense that its tuples can be deduced from the relationships stored with Person. The schema:Persons(name, childrenOfFemale, childrenOfMale)Parent-Child(parent, child)Exercise 4.4.4You get a schema like:Studios(name, address, ownedMovie)Since name -> address is the only FD, the key is {name, ownedMovie}, and the FD has a left side that is not a superkey.Exercise 4.4.5(a,b,c)(a) Struct Card { string rank, string suit };(b) class Hand {attribute Set theHand;};For part (c) we have:Hands(handId, rank, suit)Notice that the class Hand has no key, so we need to create one: handID. Each hand has, in the relation Hands, one tuple for each card in the hand.Exercise 4.4.5(e)Struct PlayerHand { string Player, Hand theHand };class Deal {attribute Set theDeal;}Alternatively, PlayerHand can be defined directly within the declaration of attribute theDeal. Exercise 4.4.5(h)Since keys for Hand and Deal are lacking, a mechanical way to design the database schema is to have one relation connecting deals and player-hand pairs, and another to specify the contents of hands. That is:Deals(dealID, player, handID)Hands(handID, rank, suit)However, if we think about it, we can get rid of handID and connect the deal and the player directly to the player's cards, as:Deals(dealID, player, rank, suit)Exercise 4.4.5(i)First, card is really a pair consisting of a suit and a rank, so we need two attributes in a relation schema to represent cards. However, much more important is the fact that the proposed schema does not distinguish which card is in which hand. Thus, we need another attribute that indicates which hand within the deal a card belongs to, something like:Deals(dealID, handID, rank, suit)Exercise 4.4.6(c)Attribute b is really a bag of (f,g) pairs. Thus, associated with each a-value will be zero or more (f,g) pairs, each of which can occur several times. We shall use an attribute count to indicate the number of occurrences, although if relations allow duplicate tuples we could simply allow duplicate (a,f,g) triples in the relation. The proposed schema is:C(a, f, g, count)Solutions for Section 4.5Exercise 4.5.1(b)Studios(name, address, movies{(title, year, inColor, length,stars{(name, address, birthdate)})})Since the information about a star is repeated once for each of their movies, there is redundancy. To eliminate it, we have to use a separate relation for stars and use pointers from studios. That is: Stars(name, address, birthdate)Studios(name, address, movies{(title, year, inColor, length,stars{*Stars})})Since each movie is owned by one studio, the information about a movie appears in only one tuple of Studios, and there is no redundancy.Exercise 4.5.2Customers(name, address, phone, ssNo, accts{*Accounts})Accounts(number, type, balance, owners{*Customers})Solutions for Section 4.6Exercise 4.6.1(a)We need to add new nodes labeled George Lucas and Gary Kurtz. Then, from the node sw (which represents the movie Star Wars), we add arcs to these two new nodes, labeled directedBy and producedBy, respectively.Exercise 4.6.2Create nodes for each account and each customer. From each customer node is an arc to a node representing the attributes of the customer, e.g., an arc labeled name to the customer's name. Likewise, there is an arc from each account node to each attribute of that account, e.g., an arc labeled balance to the value of the balance.To represent ownership of accounts by customers, we place an arc labeled owns from each customer node to the node of each account that customer holds (possibly jointly). Also, we placean arc labeled ownedBy from each account node to the customer node for each owner of that account.Exercise 4.6.5In the semistructured model, nodes represent data elements, i.e., entities rather than entity sets. In the E/R model, nodes of all types represent schema elements, and the data is not represented at all. Solutions for Section 4.7Exercise 4.7.1(a)<STARS-MOVIES><STAR starId = "cf" starredIn = "sw, esb, rj"><NAME>Carrie Fisher</NAME><ADDRESS><STREET>123 Maple St.</STREET><CITY>Hollywood</CITY></ADDRESS><ADDRESS><STREET>5 Locust Ln.</STREET><CITY>Malibu</CITY></ADDRESS></STAR><STAR starId = "mh" starredIn = "sw, esb, rj"><NAME>Mark Hamill</NAME><ADDRESS><STREET>456 Oak Rd.<STREET><CITY>Brentwood</CITY></ADDRESS></STAR><STAR starId = "hf" starredIn = "sw, esb, rj, wit"><NAME>Harrison Ford</NAME><ADDRESS><STREET>whatever</STREET><CITY>whatever</CITY></ADDRESS></STAR><MOVIE movieId = "sw" starsOf = "cf, mh"><TITLE>Star Wars</TITLE><YEAR>1977</YEAR></MOVIE><MOVIE movieId = "esb" starsOf = "cf, mh"><TITLE>Empire Strikes Back</TITLE><YEAR>1980</YEAR></MOVIE><MOVIE movieId = "rj" starsOf = "cf, mh"><TITLE>Return of the Jedi</TITLE><YEAR>1983</YEAR></MOVIE><MOVIE movieID = "wit" starsOf = "hf"><TITLE>Witness</TITLE><YEAR>1985</YEAR></MOVIE></STARS-MOVIES>Exercise 4.7.2<!DOCTYPE Bank [<!ELEMENT BANK (CUSTOMER* ACCOUNT*)><!ELEMENT CUSTOMER (NAME, ADDRESS, PHONE, SSNO)><!A TTLIST CUSTOMERcustId IDowns IDREFS><!ELEMENT NAME (#PCDATA)><!ELEMENT ADDRESS (#PCDA TA)><!ELEMENT PHONE (#PCDATA)><!ELEMENT SSNO (#PCDA TA)><!ELEMENT ACCOUNT (NUMBER, TYPE, BALANCE)><!A TTLIST ACCOUNTacctId IDownedBy IDREFS><!ELEMENT NUMBER (#PCDA TA)><!ELEMENT TYPE (#PCDA TA)><!ELEMENT BALANCE (#PCDATA)>]>BookSolutions for Chapter 5Solutions for Section 5.2Exercise 5.2.1(a)PI_model( SIGMA_{speed >= 1000} ) (PC)Exercise 5.2.1(f)The trick is to theta-join PC with itself on the condition that the hard disk sizes are equal. That gives us tuples that have two PC model numbers with the same value of hd. However, these two PC's could in fact be the same, so we must also require in the theta-join that the model numbers be unequal. Finally, we want the hard disk sizes, so we project onto hd.The expression is easiest to see if we write it using some temporary values. We start by renaming PC twice so we can talk about two occurrences of the same attributes.R1 = RHO_{PC1} (PC)R2 = RHO_{PC2} (PC)R3 = R1 JOIN_{PC1.hd = PC2.hd AND PC1.model <> PC2.model} R2R4 = PI_{PC1.hd} (R3)Exercise 5.2.1(h)First, we find R1, the model-speed pairs from both PC and Laptop. Then, we find from R1 those computers that are ``fast,'' at least 133Mh. At the same time, we join R1 with Product to connect model numbers to their manufacturers and we project out the speed to get R2. Then we join R2 with itself (after renaming) to find pairs of different models by the same maker. Finally, we get our answer, R5, by projecting onto one of the maker attributes. A sequence of steps giving the desired expression is: R1 = PI_{model,speed} (PC) UNION PI_{model,speed} (Laptop)R2 = PI_{maker,model} (SIGMA_{speed>=700} (R1) JOIN Product)R3 = RHO_{T(maker2, model2)} (R2)R4 = R2 JOIN_{maker = maker2 AND model <> model2} (R3)R5 = PI_{maker} (R4)Exercise 5.2.2Here are figures for the expression trees of Exercise 5.2.1 Part (a)Part (f)Part (h). Note that the third figure is not really a tree, since it uses a common subexpression. We could duplicate the nodes to make it a tree, but using common subexpressions is a valuable form of query optimization. One of the benefits one gets from constructing ``trees'' for queries is the ability to combine nodes that represent common subexpressions.Exercise 5.2.7The relation that results from the natural join has only one attribute from each pair of equated attributes. The theta-join has attributes for both, and their columns are identical.Exercise 5.2.9(a)If all the tuples of R and S are different, then the union has n+m tuples, and this number is the maximum possible.The minimum number of tuples that can appear in the result occurs if every tuple of one relation also appears in the other. Surely the union has at least as many tuples as the larger of R and that is, max(n,m) tuples. However, it is possible for every tuple of the smaller to appear in the other, so it is possible that there are as few as max(n,m) tuples in the union.Exercise 5.2.10In the following we use the name of a relation both as its instance (set of tuples) and as its schema (set of attributes). The context determines uniquely which is meant.PI_R(R JOIN S) Note, however, that this expression works only for sets; it does not preserve the multipicity of tuples in R. The next two expressions work for bags.R JOIN DELTA(PI_{R INTERSECT S}(S)) In this expression, each projection of a tuple from S onto the attributes that are also in R appears exactly once in the second argument of the join, so it preserves multiplicity of tuples in R, except for those thatdo not join with S, which disappear. The DELTA operator removes duplicates, as described in Section 5.4.R - [R - PI_R(R JOIN S)] Here, the strategy is to find the dangling tuples of R and remove them.Solutions for Section 5.3Exercise 5.3.1As a bag, the value is {700, 1500, 866, 866, 1000, 1300, 1400, 700, 1200, 750, 1100, 350, 733}. The order is unimportant, of course. The average is 959.As a set, the value is {700, 1500, 866, 1000, 1300, 1400, 1200, 750, 1100, 350, 733}, and the average is 967. H3>Exercise 5.3.4(a)As sets, an element x is in the left-side expression(R UNION S) UNION Tif and only if it is in at least one of R, S, and T. Likewise, it is in the right-side expressionR UNION (S UNION T)under exactly the same conditions. Thus, the two expressions have exactly the same members, and the sets are equal.As bags, an element x is in the left-side expression as many times as the sum of the number of times it is in R, S, and T. The same holds for the right side. Thus, as bags the expressions also have the same value.Exercise 5.3.4(h)As sets, element x is in the left sideR UNION (S INTERSECT T)if and only if x is either in R or in both S and T. Element x is in the right side(R UNION S) INTERSECT (R UNION T)if and only if it is in both R UNION S and R UNION T. If x is in R, then it is in both unions. If x is in both S and T, then it is in both union. However, if x is neither in R nor in both of S and T, then it cannot be in both unions. For example, suppose x is not in R and not in S. Then x is not in R UNION S. Thus, the statement of when x is in the right side is exactly the same as when it is in the left side: x is either in R or in both of S and T.Now, consider the expression for bags. Element x is in the left side the sum of the number of times it is in R plus the smaller of the number of times x is in S and the number of times x is in T. Likewise, the number of times x is in the right side is the smaller ofThe sum of the number of times x is in R and in S.The sum of the number of times x is in R and in T.A moment's reflection tells us that this minimum is the sum of the number of times x is in R plus the smaller of the number of times x is in S and in T, exactly as for the left side.Exercise 5.3.5(a)For sets, we observe that element x is in the left side(R INTERSECT S) - T。
数据库第二章课后习题解答
第3部分习题及其解答第一章的两道题3-2 习题2分别把习题、习题的ER图转换成关系模型数据结构。
【参考答案】1．习题的ER图可转换成如下的关系模型数据结构。
①程序员(编号，姓名，性别，年龄，单位，职称)，其中编号是关键字；②程序(程序名称，版权，专利号，价格)，其中程序名称是关键字；③设计(编号，程序名称，开始时间，结束时间)，其中(编号，程序名称)是关键字。
2．习题的ER 图可转换成如下的关系模型数据结构。
① 工厂(工厂名称，厂址，联系电话)，其中工厂名称是关键字； ② 产品(产品号，产品名，规格，单价)，其中产品号是关键字；③ 工人(工人编号，姓名，性别，职称，工厂名称，雇用期，月薪)，其中工人编号是关键字，工厂名称是外关键字，雇用期和月薪是联系属性；④ 生产(工厂名称，产品号，月产量)，其中(工厂名称，产品号)是关键字,生产关系是表示联系的。
判断下列情况，分别指出它们具体遵循那一类完整性约束规则1．用户写一条语句明确指定月份数据在1～12之间有效。
2．关系数据库中不允许主键值为空的元组存在。
3．从A 关系的外键出发去找B 关系中的记录，必须能找到。
【解答】1．用户用语句指定月份数据在1～12之间有效，遵循用户定义的完整性约束规则。
2．关系数据库中不允许主键值为空的元组存在，遵循实体完整性约束规则；3．从A 关系的外键出发去找B 关系的记录,必须能找到，遵循引用完整性约束规则。
判断下列情况，分别指出他们是用DML 还是用DDL 来完成下列操作1．创建“学生”表结构。
2．对“学生”表中的学号属性，其数据类型由“整型”修改为“字符型”。
3．把“学生”表中学号“021”修改为“025”。
【解答】1．创建“学生”表结构，即定义一个关系模式，用DDL 完成。
2．修改“学生”表中学号属性的数据类型,即修改关系模式的定义，用DDL 完成。
3．修改“学生”表中学号属性的数据值,即对表中的数据进行操作，用DML 完成。
数据库系统基础教程(第二版)课后习题答案2
Database Systems: The Complete BookSolutions for Chapter 2Solutions for Section 2.1Exercise 2.1.1The E/R Diagram.Exercise 2.1.8(a)The E/R DiagramKobvxybzSolutions for Section 2.2Exercise 2.2.1The Addresses entity set is nothing but a single address, so we would prefer to make address an attribute of Customers. Were the bank to record several addresses for a customer, then it might make sense to have an Addresses entity set and make Lives-at a many-many relationship.The Acct-Sets entity set is useless. Each customer has a unique account set containing his or her accounts. However, relating customers directly to their accounts in a many-many relationship conveys the same information and eliminates the account-set concept altogether.Solutions for Section 2.3Exercise 2.3.1(a)Keys ssNo and number are appropriate for Customers and Accounts, respectively. Also, we think it does not make sense for an account to be related to zero customers, so we should round the edge connecting Owns to Customers. It does not seem inappropriate to have a customer with 0 accounts;they might be a borrower, for example, so we put no constraint on the connection from Owns to Accounts. Here is the The E/R Diagram，showing underlined keys andthe numerocity constraint.Exercise 2.3.2(b)If R is many-one from E1 to E2, then two tuples (e1,e2) and (f1,f2) of the relationship set for R must be the same if they agree on the key attributes for E1. To see why, surely e1 and f1 are the same. Because R is many-one from E1 to E2, e2 and f2 must also be the same. Thus, the pairs are the same.Solutions for Section 2.4Exercise 2.4.1Here is the The E/R Diagram.We have omitted attributes other than our choice for the key attributes of Students and Courses. Also omitted are names for the relationships. Attribute grade is not part of the key for Enrollments. The key for Enrollements is studID from Students and dept and number from Courses.Exercise 2.4.4bHere is the The E/R Diagram Again, we have omitted relationship names and attributes other than our choice for the key attributes. The key for Leagues is its own name; this entity set is not weak. The key for Teams is its own name plus the name of the league of which the team is a part, e.g., (Rangers, MLB) or (Rangers, NHL). The key for Players consists of the player's number and the key for the team on which he or she plays. Since the latter key is itself a pair consisting of team and league names, the key for players is the triple (number, teamName, leagueName). e.g., JeffGarcia is (5, 49ers, NFL).Database Systems: The Complete BookSolutions for Chapter 3Solutions for Section 3.1Exercise 3.1.2(a)We can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36.Solutions for Section 3.2Exercise 3.2.1Customers(ssNo, name, address, phone)Flights(number, day, aircraft)Bookings(ssNo, number, day, row, seat)Being a weak entity set, Bookings' relation has the keys for Customers and Flights and Bookings' own attributes.Notice that the relations obtained from the toCust and toFlt relationships are unnecessary. They are:toCust(ssNo, ssNo1, number, day)toFlt(ssNo, number, day, number1, day1)That is, for toCust, the key of Customers is paired with the key for Bookings. Since both include ssNo, this attribute is repeated with two different names, ssNo and ssNo1. A similar situation exists for toFlt.Exercise 3.2.3Ships(name, yearLaunched)SisterOf(name, sisterName)Solutions for Section 3.3Exercise 3.3.1Since Courses is weak, its key is number and the name of its department. We do not have arelation for GivenBy. In part (a), there is a relation for Courses and a relation for LabCourses that has only the key and the computer-allocation attribute. It looks like:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, allocation)For part (b), LabCourses gets all the attributes of Courses, as:Depts(name, chair)Courses(number, deptName, room)LabCourses(number, deptName, room, allocation)And for (c), Courses and LabCourses are combined, as:Depts(name, chair)Courses(number, deptName, room, allocation)Exercise 3.3.4(a)There is one relation for each entity set, so the number of relations is e. The relation for the root entity set has a attributes, while the other relations, which must include the key attributes, have a+k attributes.Solutions for Section 3.4Exercise 3.4.2Surely ID is a key by itself. However, we think that the attributes x, y, and z together form another key. The reason is that at no time can two molecules occupy the same point.Exercise 3.4.4The key attributes are indicated by capitalization in the schema below:Customers(SSNO, name, address, phone)Flights(NUMBER, DAY, aircraft)Bookings(SSNO, NUMBER, DAY, row, seat)Exercise 3.4.6(a)The superkeys are any subset that contains A1. Thus, there are 2^{n-1} such subsets, since each of the n-1 attributes A2 through An may independently be chosen in or out.Solutions for Section 3.5Exercise 3.5.1(a)We could try inference rules to deduce new dependencies until we are satisfied we have them all.A more systematic way is to consider the closures of all 15 nonempty sets of attributes.For the single attributes we have A+ = A, B+ = B, C+ = ACD, and D+ = AD. Thus, the only new dependency we get with a single attribute on the left is C->A.Now consider pairs of attributes:AB+ = ABCD, so we get new dependency AB->D. AC+ = ACD, and AC->D is nontrivial. AD+ = AD, so nothing new. BC+ = ABCD, so we get BC->A, and BC->D. BD+ = ABCD, giving usBD->A and BD->C. CD+ = ACD, giving CD->A.For the triples of attributes, ACD+ = ACD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC->D, ABD->C, and BCD->A.Since ABCD+ = ABCD, we get no new dependencies.The collection of 11 new dependencies mentioned above is: C->A, AB->D, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.Exercise 3.5.1(b)From the analysis of closures above, we find that AB, BC, and BD are keys. All other sets either do not have ABCD as the closure or contain one of these three sets.Exercise 3.5.1(c)The superkeys are all those that contain one of those three keys. That is, a superkey that is not a key must contain B and more than one of A, C, and D. Thus, the (proper) superkeys are ABC, ABD, BCD, and ABCD.Exercise 3.5.3(a)We must compute the closure of A1A2...AnC. Since A1A2...An->B is a dependency, surely B is in this set, proving A1A2...AnC->B.Exercise 3.5.4(a)Consider the relationThis relation satisfies A->B but does not satisfy B->A.Exercise 3.5.8(a)If all sets of attributes are closed, then there cannot be any nontrivial functional dependenc ies. For suppose A1A2...An->B is a nontrivial dependency. Then A1A2...An+ contains B and thus A1A2...An is not closed.Exercise 3.5.10(a)We need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets: A+ = AB+ = BC+ = ACEAB+ = ABCDEAC+ = ACEBC+ = ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC are: C->A and AB->C. Note that BC->A is true, but follows logically from C->A, and therefore may be omitted from our list.Solutions for Section 3.6Exercise 3.6.1(a)In the solution to Exercise 3.5.1 we found that there are 14 nontrivial dependencies, including the three given ones and 11 derived dependencies. These are: C->A, C->D, D->A, AB->D, AB-> C, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A.We also learned that the three keys were AB, BC, and BD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. These are: C->A, C->D, D->A, AC->D, and CD->A.One choice is to decompose using C->D. That gives us ABC and CD as decomposed relations. CD is surely in BCNF, since any two-attribute relation is. ABC is not in BCNF, since AB and BC are its only keys, but C->A is a dependency that holds in ABCD and therefore holds in ABC. We must further decompose ABC into AC and BC. Thus, the three relations of the decomposition are AC, BC, and CD.Since all attributes are in at least one key of ABCD, that relation is already in 3NF, and no decomposition is necessary.Exercise 3.6.1(b)(Revised 1/19/02) The only key is AB. Thus, B->C and B->D are both BCNF violations. The derived FD's BD->C and BC->D are also BCNF violations. However, any other nontrivial, derived FD will have A and B on the left, and therefore will contain a key.One possible BCNF decomposition is AB and BCD. It is obtained starting with any of the four violations mentioned above. AB is the only key for AB, and B is the only key for BCD.Since there is only one key for ABCD, the 3NF violations are the same, and so is the decomposition.Solutions for Section 3.7Exercise 3.7.1Since A->->B, and all the tuples have the same value for attribute A, we can pair the B-value from any tuple with the value of the remaining attribute C from any other tuple. Thus, we know that R must have at least the nine tuples of the form (a,b,c), where b is any of b1, b2, or b3, and c is any of c1, c2, or c3. That is, we can derive, using the definition of a multivalued dependency, that each of the tuples (a,b1,c2), (a,b1,c3), (a,b2,c1), (a,b2,c3), (a,b3,c1), and (a,b3,c2) are also in R.Exercise 3.7.2(a)First, people have unique Social Security numbers and unique birthdates. Thus, we expect the functional dependencies ssNo->name and ssNo->birthdate hold. The same applies to children, so we expect childSSNo->childname and childSSNo->childBirthdate. Finally, an automobile has a unique brand, so we expect autoSerialNo->autoMake.There are two multivalued dependencies that do not follow from these functional dependencies. First, the information about one child of a person is independent of other information about that person. That is, if a person with social security number s has a tuple with cn,cs,cb, then if there isany other tuple t for the same person, there will also be another tuple that agrees with t except that it has cn,cs,cb in its components for the child name, Social Security number, and birthdate. That is the multivalued dependencyssNo->->childSSNo childName childBirthdateSimilarly, an automobile serial number and make are independent of any of the other attributes, so we expect the multivalued dependencyssNo->->autoSerialNo autoMakeThe dependencies are summarized below:ssNo -> name birthdatechildSSNo -> childName childBirthdateautoSerialNo -> autoMakessNo ->-> childSSNo childName childBirthdatessNo ->-> autoSerialNo autoMakeExercise 3.7.2(b)We suggest the relation schemas{ssNo, name, birthdate}{ssNo, childSSNo}{childSSNo, childName childBirthdate}{ssNo, autoSerialNo}{autoSerialNo, autoMake}An initial decomposition based on the two multivalued dependencies would give us {ssNo, name, birthDate}{ssNo, childSSNo, childName, childBirthdate}{ssNo, autoSerialNo, autoMake}Functional dependencies force us to decompose the second and third of these.Exercise 3.7.3(a)Since there are no functional dependencies, the only key is all four attributes, ABCD. Thus, each of the nontrvial multivalued dependencies A->->B and A->->C violate 4NF. We must separate out the attributes of these dependencies, first decomposing into AB and ACD, and then decomposing the latter into AC and AD because A->->C is still a 4NF violation for ACD. The final set of relations are AB, AC, and AD.Exercise 3.7.7(a)Let W be the set of attributes not in X, Y, or Z. Consider two tuples xyzw and xy'z'w' in the relation R in question. Because X ->-> Y, we can swap the y's, so xy'zw and xyz'w' are in R. Because X ->-> Z, we can take the pair of tuples xyzw and xyz'w' and swap Z's to get xyz'w and xyzw'. Similarly, we can take the pair xy'z'w' and xy'zw and swap Z's to get xy'zw' and xy'z'w.In conclusion, we started with tuples xyzw and xy'z'w' and showed that xyzw' and xy'z'w must also be in the relation. That is exactly the statement of the MVD X ->-> Y-union-Z. Note that the above statements all make sense even if there are attributes in common among X, Y, and Z.Exercise 3.7.8(a)Consider a relation R with schema ABCD and the instance with four tuples abcd, abcd', ab'c'd, and ab'c'd'. This instance satisfies the MVD A->-> BC. However, it does not satisfy A->-> B. For example, if it did satisfy A->-> B, then because the instance contains the tuples abcd and ab'c'd, we would expect it to contain abc'd and ab'cd, neither of which is in the instance.Database Systems: The Complete BookSolutions for Chapter 4Solutions for Section 4.2Exercise 4.2.1class Customer {attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account {attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Exercise 4.2.4class Person {attribute string name;relationship Person motherOfinverse Person::childrenOfFemalerelationship Person fatherOfinverse Person::childrenOfMalerelationship Set<Person> childreninverse Person::parentsOfrelationship Set<Person> childrenOfFemaleinverse Person::motherOfrelationship Set<Person> childrenOfMaleinverse Person::fatherOfrelationship Set<Person> parentsOfinverse Person::children}Notice that there are six different relationships here. For example, the inverse of the relationship that connects a person to their (unique) mother is a relationship that connects a mother (i.e., a female person) to the set of her children. That relationship, which we call childrenOfFemale, is different from the children relationship, which connects anyone -- male or female -- to their children.Exercise 4.2.7A relationship R is its own inverse if and only if for every pair (a,b) in R, the pair (b,a) is also in R. In the terminology of set theory, the relation R is ``symmetric.''Solutions for Section 4.3Exercise 4.3.1We think that Social Security number should me the key for Customer, and account number should be the key for Account. Here is the ODL solution with key and extent declarations.class Customer(extent Customers key ssNo){attribute string name;attribute string addr;attribute string phone;attribute integer ssNo;relationship Set<Account> ownsAcctsinverse Account::ownedBy;}class Account(extent Accounts key number){attribute integer number;attribute string type;attribute real balance;relationship Set<Customer> ownedByinverse Customer::ownsAccts}Solutions for Section 4.4Exercise 4.4.1(a)Since the relationship between customers and accounts is many-many, we should create a separate relation from that relationship-pair.Customers(ssNo, name, address, phone)Accounts(number, type, balance)CustAcct(ssNo, number)Exercise 4.4.1(d)Ther is only one attribute, but three pairs of relationships from Person to itself. Since motherOf and fatherOf are many-one, we can store their inverses in the relation for Person. That is, for each person, childrenOfMale and childrenOfFemale will indicate that persons's father and mother. The children relationship is many-many, and requires its own relation. This relation actually turns out to be redundant, in the sense that its tuples can be deduced from the relationships stored with Person. The schema:Persons(name, childrenOfFemale, childrenOfMale)Parent-Child(parent, child)Exercise 4.4.4Y ou get a schema like:Studios(name, address, ownedMovie)Since name -> address is the only FD, the key is {name, ownedMovie}, and the FD has a left side that is not a superkey.Exercise 4.4.5(a,b,c)(a) Struct Card { string rank, string suit };(b) class Hand {attribute Set theHand;};For part (c) we have:Hands(handId, rank, suit)Notice that the class Hand has no key, so we need to create one: handID. Each hand has, in the relation Hands, one tuple for each card in the hand.Exercise 4.4.5(e)Struct PlayerHand { string Player, Hand theHand };class Deal {attribute Set theDeal;}Alternatively, PlayerHand can be defined directly within the declaration of attribute theDeal. Exercise 4.4.5(h)Since keys for Hand and Deal are lacking, a mechanical way to design the database schema is to have one relation connecting deals and player-hand pairs, and another to specify the contents of hands. That is:Deals(dealID, player, handID)Hands(handID, rank, suit)However, if we think about it, we can get rid of handID and connect the deal and the player directly to the player's cards, as:Deals(dealID, player, rank, suit)Exercise 4.4.5(i)First, card is really a pair consisting of a suit and a rank, so we need two attributes in a relation schema to represent cards. However, much more important is the fact that the proposed schema does not distinguish which card is in which hand. Thus, we need another attribute that indicates which hand within the deal a card belongs to, something like:Deals(dealID, handID, rank, suit)Exercise 4.4.6(c)Attribute b is really a bag of (f,g) pairs. Thus, associated with each a-value will be zero or more (f,g) pairs, each of which can occur several times. We shall use an attribute count to indicate the number of occurrences, although if relations allow duplicate tuples we could simply allow duplicate (a,f,g) triples in the relation. The proposed schema is:C(a, f, g, count)Solutions for Section 4.5Exercise 4.5.1(b)Studios(name, address, movies{(title, year, inColor, length,stars{(name, address, birthdate)})})Since the information about a star is repeated once for each of their movies, there is redundancy. To eliminate it, we have to use a separate relation for stars and use pointers from studios. That is: Stars(name, address, birthdate)Studios(name, address, movies{(title, year, inColor, length,stars{*Stars})})Since each movie is owned by one studio, the information about a movie appears in only one tuple of Studios, and there is no redundancy.Exercise 4.5.2Customers(name, address, phone, ssNo, accts{*Accounts})Accounts(number, type, balance, owners{*Customers})Solutions for Section 4.6Exercise 4.6.1(a)We need to add new nodes labeled George Lucas and Gary Kurtz. Then, from the node sw (which represents the movie Star Wars), we add arcs to these two new nodes, labeled direc tedBy and producedBy, respectively.Exercise 4.6.2Create nodes for each account and each customer. From each customer node is an arc to a node representing the attributes of the customer, e.g., an arc labeled name to the customer's name. Likewise, there is an arc from each account node to each attribute of that account, e.g., an arc labeled balance to the value of the balance.To represent ownership of accounts by customers, we place an arc labeled owns from each customer node to the node of each account that customer holds (possibly jointly). Also, we placean arc labeled ownedBy from each account node to the customer node for each owner of that account.Exercise 4.6.5In the semistructured model, nodes represent data elements, i.e., entities rather than entity sets. In the E/R model, nodes of all types represent schema elements, and the data is not represented at all. Solutions for Section 4.7Exercise 4.7.1(a)<STARS-MOVIES><STAR starId = "cf" starredIn = "sw, esb, rj"><NAME>Carrie Fisher</NAME><ADDRESS><STREET>123 Maple St.</STREET><CITY>Hollywood</CITY></ADDRESS><ADDRESS><STREET>5 Locust Ln.</STREET><CITY>Malibu</CITY></ADDRESS></STAR><STAR starId = "mh" starredIn = "sw, esb, rj"><NAME>Mark Hamill</NAME><ADDRESS><STREET>456 Oak Rd.<STREET><CITY>Brentwood</CITY></ADDRESS></STAR><STAR starId = "hf" starredIn = "sw, esb, rj, wit"><NAME>Harrison Ford</NAME><ADDRESS><STREET>whatever</STREET><CITY>whatever</CITY></ADDRESS></STAR><MOVIE movieId = "sw" starsOf = "cf, mh"><TITLE>Star Wars</TITLE><YEAR>1977</YEAR></MOVIE><MOVIE movieId = "esb" starsOf = "cf, mh"><TITLE>Empire Strikes Back</TITLE><YEAR>1980</YEAR></MOVIE><MOVIE movieId = "rj" starsOf = "cf, mh"><TITLE>Return of the Jedi</TITLE><YEAR>1983</YEAR></MOVIE><MOVIE movieID = "wit" starsOf = "hf"><TITLE>Witness</TITLE><YEAR>1985</YEAR></MOVIE></STARS-MOVIES>Exercise 4.7.2<!DOCTYPE Bank [<!ELEMENT BANK (CUSTOMER* ACCOUNT*)><!ELEMENT CUSTOMER (NAME, ADDRESS, PHONE, SSNO)> <!A TTLIST CUSTOMERcustId IDowns IDREFS><!ELEMENT NAME (#PCDA TA)><!ELEMENT ADDRESS (#PCDA TA)><!ELEMENT PHONE (#PCDA TA)><!ELEMENT SSNO (#PCDA TA)><!ELEMENT ACCOUNT (NUMBER, TYPE, BALANCE)><!A TTLIST ACCOUNTacctId IDownedBy IDREFS><!ELEMENT NUMBER (#PCDA TA)><!ELEMENT TYPE (#PCDA TA)><!ELEMENT BALANCE (#PCDA TA)>]>Database Systems: The CompleteBookSolutions for Chapter 5Solutions for Section 5.2Exercise 5.2.1(a)PI_model( SIGMA_{speed >= 1000} ) (PC)Exercise 5.2.1(f)The trick is to theta-join PC with itself on the condition that the hard disk sizes are equal. That gives us tuples that have two PC model numbers with the same value of hd. However, these two PC's could in fact be the same, so we must also require in the theta-join that the model numbers be unequal. Finally, we want the hard disk sizes, so we project onto hd.The expression is easiest to see if we write it using some temporary values. We start by renaming PC twice so we can talk about two occurrences of the same attributes.R1 = RHO_{PC1} (PC)R2 = RHO_{PC2} (PC)R3 = R1 JOIN_{PC1.hd = PC2.hd AND PC1.model <> PC2.model} R2R4 = PI_{PC1.hd} (R3)Exercise 5.2.1(h)First, we find R1, the model-speed pairs from both PC and Laptop. Then, we find from R1 those computers that are ``fast,'' at least 133Mh. At the same time, we join R1 with Product to connect model numbers to their manufacturers and we project out the speed to get R2. Then we join R2 with itself (after renaming) to find pairs of different models by the same maker. Finally, we get our answer, R5, by projecting onto one of the maker attributes. A sequence of steps giving the desired expression is: R1 = PI_{model,speed} (PC) UNION PI_{model,speed} (Laptop)R2 = PI_{maker,model} (SIGMA_{speed>=700} (R1) JOIN Product)R3 = RHO_{T(maker2, model2)} (R2)R4 = R2 JOIN_{maker = maker2 AND model <> model2} (R3)R5 = PI_{maker} (R4)Exercise 5.2.2Here are figures for the expression trees of Exercise 5.2.1 Part (a)Part (f)Part (h). Note that the third figure is not really a tree, since it uses a common subexpression. We could duplicate the nodes to make it a tree, but using common subexpressions is a valuable form of query optimization. One of the benefits one gets from constructing ``trees'' for queries is the ability to combine nodes that represent common subexpressions.Exercise 5.2.7The relation that results from the natural join has only one attribute from each pair of equated attributes. The theta-join has attributes for both, and their columns are identical.Exercise 5.2.9(a)If all the tuples of R and S are different, then the union has n+m tuples, and this number is the maximum possible.The minimum number of tuples that can appear in the result occurs if every tuple of one relation also appears in the other. Surely the union has at least as many tuples as the larger of R and that is, max(n,m) tuples. However, it is possible for every tuple of the smaller to appear in the other, so it is possible that there are as few as max(n,m) tuples in the union.Exercise 5.2.10In the following we use the name of a relation both as its instance (set of tuples) and as its schema (set of attributes). The context determines uniquely which is meant.PI_R(R JOIN S) Note, however, that this expression works only for sets; it does not preserve the multipicity of tuples in R. The next two expressions work for bags.R JOIN DELTA(PI_{R INTERSECT S}(S)) In this expression, each projection of a tuple from S onto the attributes that are also in R appears exactly once in the second argument of the join, so it preserves multiplicity of tuples in R, except for those thatdo not join with S, which disappear. The DELTA operator removes duplicates, as described in Section 5.4.R - [R - PI_R(R JOIN S)] Here, the strategy is to find the dangling tuples of R and remove them.Solutions for Section 5.3Exercise 5.3.1As a bag, the value is {700, 1500, 866, 866, 1000, 1300, 1400, 700, 1200, 750, 1100, 350, 733}. The order is unimportant, of course. The average is 959.As a set, the value is {700, 1500, 866, 1000, 1300, 1400, 1200, 750, 1100, 350, 733}, and the average is 967. H3>Exercise 5.3.4(a)As sets, an element x is in the left-side expression(R UNION S) UNION Tif and only if it is in at least one of R, S, and T. Likewise, it is in the right-side expressionR UNION (S UNION T)under exactly the same conditions. Thus, the two expressions have exactly the same members, and the sets are equal.As bags, an element x is in the left-side expression as many times as the sum of the number of times it is in R, S, and T. The same holds for the right side. Thus, as bags the expressions also have the same value.Exercise 5.3.4(h)As sets, element x is in the left sideR UNION (S INTERSECT T)if and only if x is either in R or in both S and T. Element x is in the right side(R UNION S) INTERSECT (R UNION T)if and only if it is in both R UNION S and R UNION T. If x is in R, then it is in both unions. If x is in both S and T, then it is in both union. However, if x is neither in R nor in both of S and T, then it cannot be in both unions. For example, suppose x is not in R and not in S. Then x is not in R UNION S. Thus, the statement of when x is in the right side is exactly the same as when it is in the left side: x is either in R or in both of S and T.Now, consider the expression for bags. Element x is in the left side the sum of the number of times it is in R plus the smaller of the number of times x is in S and the number of times x is in T. Likewise, the number of times x is in the right side is the smaller ofThe sum of the number of times x is in R and in S.The sum of the number of times x is in R and in T.A moment's reflection tells us that this minimum is the sum of the number of times x is in R plus the smaller of the number of times x is in S and in T, exactly as for the left side.Exercise 5.3.5(a)For sets, we observe that element x is in the left side(R INTERSECT S) - T。
(完整版)数据库系统基础教程第二章答案解析
For relation Accounts, the attributes are:acctNo, type, balanceFor relation Customers, the attributes are:firstName, lastName, idNo, accountExercise 2.2.1bFor relation Accounts, the tuples are:(12345, savings, 12000),(23456, checking, 1000),(34567, savings, 25)For relation Customers, the tuples are:(Robbie, Banks, 901-222, 12345),(Lena, Hand, 805-333, 12345),(Lena, Hand, 805-333, 23456)Exercise 2.2.1cFor relation Accounts and the first tuple, the components are:123456 → acctNosavings → type12000 → balanceFor relation Customers and the first tuple, the components are:Robbie → firstNameBanks → lastName901-222 → idNo12345 → accountExercise 2.2.1dFor relation Accounts, a relation schema is:Accounts(acctNo, type, balance)For relation Customers, a relation schema is:Customers(firstName, lastName, idNo, account) Exercise 2.2.1eAn example database schema is:Accounts (acctNo,type,balance)Customers (firstName,lastName,idNo,account)A suitable domain for each attribute:acctNo → Integertype → Stringbalance → IntegerfirstName → StringlastName → StringidNo → String (because there is a hyphen we cannot use Integer)account → IntegerExercise 2.2.1gAnother equivalent way to present the Account relation:Another equivalent way to present the Customers relation:Exercise 2.2.2Examples of attributes that are created for primarily serving as keys in a relation:Universal Product Code (UPC) used widely in United States and Canada to track products in stores.Serial Numbers on a wide variety of products to allow the manufacturer to individually track each product.Vehicle Identification Numbers (VIN), a unique serial number used by the automotive industry to identify vehicles.Exercise 2.2.3aWe can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36.Exercise 2.2.3bWe can order the three tuples in any of 5! = 120 ways. Also, the columns can be ordered in any of 4! = 24 ways. Thus, the number of presentations is 120*24 = 2880Exercise 2.2.3cWe can order the three tuples in any of m! ways. Also, the columns can be ordered in any of n! ways. Thus, the number of presentations is n!m!Exercise 2.3.1aCREATE TABLE Product (maker CHAR(30),model CHAR(10) PRIMARY KEY,type CHAR(15));CREATE TABLE PC (model CHAR(30),speed DECIMAL(4,2),ram INTEGER,hd INTEGER,price DECIMAL(7,2));Exercise 2.3.1cCREATE TABLE Laptop (model CHAR(30),speed DECIMAL(4,2),ram INTEGER,hd INTEGER,screen DECIMAL(3,1),price DECIMAL(7,2));Exercise 2.3.1dCREATE TABLE Printer (model CHAR(30),color BOOLEAN,type CHAR (10),price DECIMAL(7,2));Exercise 2.3.1eALTER TABLE Printer DROP color;Exercise 2.3.1fALTER TABLE Laptop ADD od CHAR (10) DEFAULT ‘none’; Exercise 2.3.2aCREATE TABLE Classes (class CHAR(20),type CHAR(5),country CHAR(20),numGuns INTEGER,bore DECIMAL(3,1),displacement INTEGER);Exercise 2.3.2bCREATE TABLE Ships (name CHAR(30),class CHAR(20),launched INTEGER);Exercise 2.3.2cCREATE TABLE Battles (name CHAR(30),date DATE);Exercise 2.3.2dCREATE TABLE Outcomes (ship CHAR(30),battle CHAR(30),result CHAR(10));Exercise 2.3.2eALTER TABLE Classes DROP bore;Exercise 2.3.2fALTER TABLE Ships ADD yard CHAR(30); Exercise 2.4.1aR1 := σspeed ≥ 3.00 (PC)R2 := πmodel(R1)model100510061013Exercise 2.4.1bR1 := σhd ≥ 100 (Laptop)R2 := Product (R1)R3 := πmaker (R2)makerEABFGExercise 2.4.1cR1 := σmaker=B (Product PC)R2 := σmaker=B (Product Laptop)R3 := σmaker=B (Product Printer)R4 := πmodel,price (R1)R5 := πmodel,price (R2)R6: = πmodel,price (R3)R7 := R4 R5 R6model price1004 6491005 6301006 10492007 1429Exercise 2.4.1dR1 := σcolor = true AND type = laser (Printer)R2 := πmodel (R1)model30033007Exercise 2.4.1eR1 := σtype=laptop (Product)R2 := σtype=PC(Product)R3 := πmaker(R1)R4 := πmaker(R2)R5 := R3 – R4Exercise 2.4.1fR1 := ρPC1(PC)R2 := ρPC2(PC)R3 := R1 (PC1.hd = PC2.hd AND PC1.model <> PC2.model) R2R4 := πhd(R3)Exercise 2.4.1gR1 := ρPC1(PC)R2 := ρPC2(PC)R3 := R1 (PC1.speed = PC2.speed AND PC1.ram = PC2.ram AND PC1.model < PC2.model) R2R4 := πPC1.model,PC2.model(R3)Exercise 2.4.1hR1 := πmodel(σspeed ≥ 2.80(PC)) πmodel(σspeed ≥ 2.80(Laptop))R2 := πmaker,model(R1 Product)R3 := ρR3(maker2,model2)(R2)R4 := R2 (maker = maker2 AND model <> model2) R3R5 := πmaker(R4)Exercise 2.4.1iR1 := πmodel,speed(PC)R2 := πmodel,speed(Laptop)R3 := R1 R2R4 := ρR4(model2,speed2)(R3)R5 := πmodel,speed (R3 (speed < speed2 ) R4)R6 := R3 – R5makerBExercise 2.4.1jR1 := πmaker,speed(Product PC)R2 := ρR2(maker2,speed2)(R1)R3 := ρR3(maker3,speed3)(R1)R4 := R1 (maker = maker2 AND speed <> speed2) R2R5 := R4 (maker3 = maker AND speed3 <> speed2 AND speed3 <> speed) R3R6 := πmaker(R5)makerFGhd25080160PC1.model PC2.model1004 1012makerBEmakerADEExercise 2.4.1kR1 := πmaker,model(Product PC)R2 := ρR2(maker2,model2)(R1)R3 := ρR3(maker3,model3)(R1)R4 := ρR4(maker4,model4)(R1)R5 := R1 (maker = maker2 AND model <> model2) R2R6 := R3 (maker3 = maker AND model3 <> model2 AND model3 <> model) R5R7 := R4 (maker4 = maker AND (model4=model OR model4=model2 OR model4=model3)) R6R8 := πmaker(R7)makerABDEExercise 2.4.2aπmodelσspeed≥3.00PCExercise 2.4.2bπmakerσhd ≥ 100 ProductLaptopExercise 2.4.2cσmaker=B πmodel,priceσmaker=B πmodel,price σmaker=Bπmodel,priceProduct PC Laptop Printer ProductProductExercise 2.4.2dPrinter σcolor = true AND type = laserπmodelExercise 2.4.2e σtype=laptop σtype=PC πmakerπmaker –Product ProductExercise 2.4.2fρPC1ρPC2 (PC1.hd = PC2.hd AND PC1.model <> PC2.model)πhdPC PCExercise 2.4.2gρPC1ρPC2PC PC(PC1.speed = PC2.speed AND PC1.ram = PC2.ram AND PC1.model < PC2.model)πPC1.model,PC2.modelExercise 2.4.2hPC Laptop σspeed ≥ 2.80σspeed ≥ 2.80πmodelπmodel πmaker,modelρR3(maker2,model2)(maker = maker2 AND model <> model2)makerExercise 2.4.2iPCLaptopProductπmodel,speed πmodel,speed ρR4(model2,speed2)πmodel,speed(speed < speed2 )–makerExercise 2.4.2jProduct PC πmaker,speed ρR3(maker3,speed3)ρR2(maker2,speed2)(maker = maker2 AND speed <> speed2)(maker3 = maker AND speed3 <> speed2 AND speed3 <> speed)πmakerExercise 2.4.2kπmaker(maker4 = maker AND (model4=model OR model4=model2 OR model4=model3)) (maker3 = maker AND model3 <> model2 AND model3 <> model)(maker = maker2 AND model <> model2)ρR2(maker2,model2)ρR3(maker3,model3)ρR4(maker4,model4)πmaker,modelProduct PCExercise 2.4.3aR1 := σbore ≥ 16 (Classes)R2 := πclass,country (R1)Exercise 2.4.3bR1 := σlaunched < 1921 (Ships)R2 := πname (R1)KirishimaKongoRamilliesRenownRepulseResolutionRevengeRoyal OakRoyal SovereignTennesseeExercise 2.4.3cR1 := σbattle=Denmark Strait AND result=sunk(Outcomes)R2 := πship (R1)shipBismarckHoodExercise 2.4.3dR1 := Classes ShipsR2 := σlaunched > 1921 AND displacement > 35000 (R1)R3 := πname (R2)nameIowaMissouriMusashiNew JerseyNorth CarolinaWashingtonWisconsinYamatoExercise 2.4.3eR1 := σbattle=Guadalcanal(Outcomes)R2 := Ships (ship=name) R1R3 := Classes R2R4 := πname,displacement,numGuns(R3)name displacement numGuns Kirishima 32000 8Washington 37000 9Exercise 2.4.3fR1 := πname(Ships)R2 := πship(Outcomes)R3 := ρR3(name)(R2)R4 := R1 R3nameCaliforniaHarunaHieiIowaKirishimaKongoMissouriMusashiNew JerseyExercise 2.4.3gFrom 2.3.2, assuming that every class has one ship named after the class.R1 := πclass (Classes) R2 := πclass (σname <> class (Ships)) R3 := R1 – R2Exercise 2.4.3hR1 := πcountry (σtype=bb (Classes)) R2 := πcountry (σtype=bc (Classes)) R3 := R1 ∩ R2Exercise 2.4.3iR1 := πship,result,date (Battles (battle=name) Outcomes)R2 := ρR2(ship2,result2,date2)(R1)R3 := R1 (ship=ship2 AND result=damaged AND date < date2) R2R4 := πship (R3)No results from sample data.Exercise 2.4.4aσbore ≥ 16πclass,countryClassesExercise 2.4.4bNorth Carolina Ramillies Renown Repulse Resolution Revenge Royal Oak Royal Sovereign Tennessee Washington Wisconsin Yamato Arizona Bismarck Duke of York Fuso Hood King George V Prince of Wales Rodney Scharnhorst South Dakota West Virginia Yamashiro class Bismarck country Japan Gt. Britainπnameσlaunched < 1921ShipsExercise 2.4.4cπshipσbattle=Denmark Strait AND result=sunkOutcomesExercise 2.4.4dπnameσlaunched > 1921 AND displacement > 35000Classes Ships Exercise 2.4.4eσbattle=Guadalcanal Outcomes Ships(ship=name)πname,displacement,numGunsExercise 2.4.4f Ships Outcomesπnameπship ρR3(name)Exercise 2.4.4g Classes Shipsπclass σname <> class πclass–Exercise 2.4.4hClasses Classesσtype=bb σtype=bcπcountry πcountry∩Exercise 2.4.4iBattles Outcomes (battle=name)πship,result,dateρR2(ship2,result2,date2)(ship=ship2 AND result=damaged AND date < date2)πshipExercise 2.4.5The result of the natural join has only one attribute from each pair of equated attributes. On the other hand, the result of the theta-join has both columns of the attributes and their values are identical.Exercise 2.4.6UnionIf we add a tuple to the arguments of the union operator, we will get all of the tuples of the original result and maybe the added tuple. If the added tuple is a duplicate tuple, then the set behavior will eliminate that tuple.Thus the union operator is monotone.IntersectionIf we add a tuple to the arguments of the intersection operator, we will get all of the tuples of the originalresult and maybe the added tuple. If the added tuple does not exist in the relation that it is added but does exist in the other relation, then the result set will include the added tuple. Thus the intersection operator is monotone.DifferenceIf we add a tuple to the arguments of the difference operator, we may not get all of the tuples of the originalresult. Suppose we have relations R and S and we are computing R – S. Suppose also that tuple t is in R but not in S. The result of R – S would include tuple t. However, if we add tuple t to S, then the new result will not have tuple t. Thus the difference operator is not monotone.ProjectionIf we add a tuple to the arguments of the projection operator, we will get all of the tuples of the original result and the projection of the added tuple. The projection operator only selects columns from the relation and does not affect the rows that are selected. Thus the projection operator is monotone.SelectionIf we add a tuple to the arguments of the selection operator, we will get all of the tuples of the original result and maybe the added tuple. If the added tuple satisfies the select condition, then it will be added to the newresult. The original tuples are included in the new result because they still satisfy the select condition. Thusthe selection operator is monotone.Cartesian ProductIf we add a tuple to the arguments of the Cartesian product operator, we will get all of the tuples of the original result and possibly additional tuples. The Cartesian product pairs the tuples of one relation with the tuples ofanother relation. Suppose that we are calculating R x S where R has m tuples and S has n tuples. If we add a tuple to R that is not already in R, then we expect the result of R x S to have (m + 1) * n tuples. Thus the Cartesianproduct operator is monotone.Natural JoinsIf we add a tuple to the arguments of a natural join operator, we will get all of the tuples of the original result and possibly additional tuples. The new tuple can only create additional successful joins, not less. If, however, the added tuple cannot successfully join with any of the existing tuples, then we will have zero additionalsuccessful joins. Thus the natural join operator is monotone.Theta JoinsIf we add a tuple to the arguments of a theta join operator, we will get all of the tuples of the original result and possibly additional tuples. The theta join can be modeled by a Cartesian product followed by a selection onsome condition. The new tuple can only create additional tuples in the result, not less. If, however, the addedtuple does not satisfy the select condition, then no additional tuples will be added to the result. Thus the theta join operator is monotone.RenamingIf we add a tuple to the arguments of a renaming operator, we will get all of the tuples of the original result and the added tuple. The renaming operator does not have any effect on whether a tuple is selected or not. In fact, the renaming operator will always return as many tuples as its argument. Thus the renaming operator is monotone.Exercise 2.4.7aIf all the tuples of R and S are different, then the union has n + m tuples, and this number is the maximum possible.The minimum number of tuples that can appear in the result occurs if every tuple of one relation also appears in the other. Then the union has max(m , n) tuples.Exercise 2.4.7bIf all the tuples in one relation can pair successfully with all the tuples in the other relation, then the natural join has n * m tuples. This number would be the maximum possible.The minimum number of tuples that can appear in the result occurs if none of the tuples of one relation can pairsuccessfully with all the tuples in the other relation. Then the natural join has zero tuples.Exercise 2.4.7cIf the condition C brings back all the tuples of R, then the cross product will contain n * m tuples. This number would be the maximum possible.The minimum number of tuples that can appear in the result occurs if the condition C brings back none of the tuples of R. Then the cross product has zero tuples.Exercise 2.4.7dAssuming that the list of attributes L makes the resulting relation πL(R) and relation S schema compatible, then the maximum possible tuples is n. This happens when all of the tuples of πL(R) are not in S.The minimum number of tuples that can appear in the result occurs when all of the tuples in πL(R) appear in S. Then the difference has max(n–m , 0) tuples.Exercise 2.4.8Defining r as the schema of R and s as the schema of S:1.πr(R S)2.R δ(πr∩s(S)) where δ is the duplicate-elimination operator in Section 5.2 pg. 2133.R – (R –πr(R S))Exercise 2.4.9Defining r as the schema of R1.R - πr(R S)Exercise 2.4.10πA1,A2…An(R S)Exercise 2.5.1aσspeed < 2.00 AND price > 500(PC) = øModel 1011 violates this constraint.Exercise 2.5.1bσscreen < 15.4 AND hd < 100 AND price ≥ 1000(Laptop) = øModel 2004 violates the constraint.Exercise 2.5.1cπmaker(σtype = laptop(Product)) ∩ πmaker(σtype = pc(Product)) = øManufacturers A,B,E violate the constraint.Exercise 2.5.1dThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R4 that stand for nodes of expression trees. Here is the sequence:R1(maker, model, speed) := πmaker,model,speed(Product PC)R2(maker, speed) := πmaker,speed(Product Laptop)R3(model) := πmodel(R1 R1.maker = R2.maker AND R1.speed ≤ R2.speed R2)R4(model) := πmodel(PC)The constraint is R4 ⊆ R3Manufacturers B,C,D violate the constraint.Exercise 2.5.1eπmodel(σLaptop.ram > PC.ram AND Laptop.price ≤ PC.price(PC × Laptop)) = øModels 2002,2006,2008 violate the constraint.Exercise 2.5.2aπclass(σbore > 16(Classes)) = øThe Yamato class violates the constraint.Exercise 2.5.2bπclass(σnumGuns > 9 AND bore > 14(Classes)) = øNo violations to the constraint.Exercise 2.5.2cThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R5 that stand for nodes of expression trees. Here is the sequence:R1(class,name) := πclass,name(Classes Ships)R2(class2,name2) := ρR2(class2,name2)(R1)R3(class3,name3) := ρR3(class3,name3)(R1)R4(class,name,class2,name2) := R1 (class = class2 AND name <> name2) R2R5(class,name,class2,name2,class3,name3) := R4 (class=class3 AND name <> name3 AND name2 <> name3) R3The constraint is R5 = øThe Kongo, Iowa and Revenge classes violate the constraint.Exercise 2.5.2dπcountry(σtype = bb(Classes)) ∩ πcountry(σtype = bc(Classes)) = øJapan and Gt. Britain violate the constraint.Exercise 2.5.2eThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R5 that stand for nodes of expression trees. Here is the sequence:R1(ship,bat tle,result,class) := πship,battle,result,class(Outcomes (ship = name) Ships)R2(ship,battle,result,numGuns) := πship,battle,result,numGuns(R1 Classes)R3(ship,battle) := πship,battle(σnumGuns < 9 AND result = sunk (R2))R4(ship2,battle2) := ρR4(ship2,battle2)(πship,battle(σnumGuns > 9(R2)))R5(ship2) := πship2(R3 (battle = battle2) R4)The constraint is R5 = øNo violations to the constraint. Since there are some ships in the Outcomes table that are not in the Ships table, we are unable to determine the number of guns on that ship.Exercise 2.5.3Defining r as the schema A1,A2,…,A n and s as the schema B1,B2,…,B n:πr(R) πs(S) = øwhere is the antisemijoinExercise 2.5.4The form of a constraint as E1 = E2 can be expressed as the other two constraints.Using the “equating an expression to the empty set” method, we can simply say:E1– E2 = øAs a containment, we can simply say:E1⊆ E2 AND E2⊆ E1Thus, the form E1 = E2 of a constraint cannot express more than the two other forms discussed in this section.。
数据库系统原理教程习题答案第2章习题
第2章关系数据库1 ．试述关系模型的三个组成部分。
答：关系模型由关系数据结构、关系操作集合和关系完整性约束三部分组成。
2 ．试述关系数据语言的特点和分类。
答：关系数据语言可以分为三类：关系代数语言。
关系演算语言：元组关系演算语言和域关系演算语言。
SQL：具有关系代数和关系演算双重特点的语言。
这些关系数据语言的共同特点是，语言具有完备的表达能力，是非过程化的集合操作语言，功能强，能够嵌入高级语言中使用。
4 ．试述关系模型的完整性规则。
在参照完整性中，为什么外部码属性的值也可以为空？什么情况下才可以为空？答：实体完整性规则是指若属性A是基本关系R的主属性，则属性A不能取空值。
若属性(或属性组)F是基本关系R的外码，它与基本关系S的主码Ks相对应(基本关系R和S不一定是不同的关系)，则对于R中每个元组在F上的值必须为：或者取空值(F的每个属性值均为空值)；或者等于S中某个元组的主码值。
即属性F本身不是主属性，则可以取空值，否则不能取空值。
5．设有一个SPJ数据库，包括S，P，J，SPJ四个关系模式：1）求供应工程J1零件的供应商号码SNO：πSno(σSno=‘J1’（SPJ）)2）求供应工程J1零件P1的供应商号码SNO：πSno(σSno=‘J1’∧Pno=‘P1‘(SPJ))3）求供应工程J1零件为红色的供应商号码SNO：πSno(σPno=‘P1‘（σCOLOR=’红‘（P）∞SPJ）)4）求没有使用天津供应商生产的红色零件的工程号JNO：πJno(SPJ)- πJNO（σcity=‘天津’∧Color=‘红‘（S∞SPJ∞P）5）求至少用了供应商S1所供应的全部零件的工程号JNO：πJno，Pno(SPJ)÷πPno（σSno=‘S1‘（SPJ））6．试述等值连接与自然连接的区别和联系。
答：连接运算符是“=”的连接运算称为等值连接。
它是从关系R与S的广义笛卡尔积中选取A，B属性值相等的那些元组自然连接是一种特殊的等值连接，它要求两个关系中进行比较的分量必须是相同的属性组，并且在结果中把重复的属性列去掉。
数据库系统教程课后答案(施伯乐)(第二版)
目录第1部分课程的教与学第2部分各章习题解答及自测题第1章数据库概论1.1 基本内容分析1.2 教材中习题1的解答1.3 自测题1.4 自测题答案第2章关系模型和关系运算理论2.1基本内容分析2.2 教材中习题2的解答2.3 自测题2.4 自测题答案第3章关系数据库语言SQL3.1基本内容分析3.2 教材中习题3的解答3.3 自测题3.4 自测题答案第4章关系数据库的规范化设计4.1基本内容分析4.2 教材中习题4的解答4.3 自测题4.4 自测题答案第5章数据库设计与ER模型5.1基本内容分析5.2 教材中习题5的解答5.3 自测题5.4 自测题答案第6章数据库的存储结构6.1基本内容分析6.2 教材中习题6的解答第7章系统实现技术7.1基本内容分析7.2 教材中习题7的解答7.3 自测题7.4 自测题答案第8章对象数据库系统8.1基本内容分析8.2 教材中习题8的解答8.3 自测题8.4 自测题答案第9章分布式数据库系统9.1基本内容分析9.2 教材中习题9的解答9.3 自测题9.4 自测题答案第10章中间件技术10.1基本内容分析10.2 教材中习题10的解答10.3 自测题及答案第11章数据库与WWW11.1基本内容分析11.2 教材中习题11的解答第12章 XML技术12.1基本内容分析12.2 教材中习题12的解答学习推荐书目1．国内出版的数据库教材（1）施伯乐,丁宝康,汪卫. 数据库系统教程(第2版). 北京:高等教育出版社,2003（2）丁宝康,董健全. 数据库实用教程(第2版). 北京:清华大学出版社,2003（3）施伯乐,丁宝康. 数据库技术. 北京:科学出版社,2002（4）王能斌. 数据库系统教程(上、下册). 北京:电子工业出版社,2002（5）闪四清. 数据库系统原理与应用教程. 北京:清华大学出版社,2001（6）萨师煊,王珊. 数据库系统概论(第3版). 北京:高等教育出版社,2000（7）庄成三,洪玫,杨秋辉. 数据库系统原理及其应用. 北京:电子工业出版社,20002．出版的国外数据库教材（中文版或影印版）（1）Silberschatz A，Korth H F，Sudarshan S. 数据库系统概念(第4版). 杨冬青,唐世渭等译. 北京:机械工业出版社,2003（2）Elmasri R A，Navathe S B. 数据库系统基础(第3版). 邵佩英,张坤龙等译. 北京:人民邮电出版社,2002（3）Lewis P M,Bernstein A,Kifer M. Databases and Transaction Processing:An Application-Oriented Approach, Addison-Wesley, 2002（影印版, 北京:高等教育出版社；中文版，施伯乐等译，即将由电子工业出版社出版）（4）Hoffer J A,Prescott M B,McFadden F R. Modern Database Management. 6th ed. Prentice Hall, 2002（中文版，施伯乐等译，即将由电子工业出版社出版）3．上机实习教材（1）廖疆星,张艳钗,肖金星. PowerBuilder 8.0 & SQL Server 2000数据库管理系统管理与实现. 北京:冶金工业出版社,2002（2）伍俊良. PowerBuilder课程设计与系统开发案例. 北京:清华大学出版社,20034．学习指导书（1）丁宝康,董健全,汪卫,曾宇昆. 数据库系统教程习题解答及上机指导. 北京:高等教育出版社,2003（2）丁宝康,张守志,严勇. 数据库技术学习指导书. 北京:科学出版社,2003（3）丁宝康,董健全,曾宇昆. 数据库实用教程习题解答. 北京:清华大学出版社,2003 （4）丁宝康. 数据库原理题典. 长春:吉林大学出版社,2002（5）丁宝康,陈坚,许建军,楼晓鸿. 数据库原理辅导与练习. 北京:经济科学出版社,2001第1部分课程的教与学1．课程性质与设置目的现在，数据库已是信息化社会中信息资源与开发利用的基础，因而数据库是计算机教育的一门重要课程，是高等院校计算机和信息类专业的一门专业基础课。
数据库系统原理第二章基本概念及课后习题有答案
数据库系统原理第二章基本概念及课后习题有答案一、数据库系统生存期1．数据库系统生存期：数据库应用系统从开始规划、设计、实现、维护到最后被新的系统取代而停止使用的整个期间。
2．数据库系统生存期分七个阶段：规划、需求分析、概念设计、逻辑设计、物理设计、实现、运行维护。
3．规划阶段三个步骤：系统调查、可行性分析、确定数据库系统总目标。
4．需求分析阶段：主要任务是系统分析员和用户双方共同收集数据库系统所需要的信息内容和用户对处理的需求，并以需求说明书的形式确定下来。
5．概念设计阶段：产生反映用户单位信息需求的概念模型。
与硬件和DBMS无关。
6．逻辑设计阶段：将概念模型转换成DBMS能处理的逻辑模型。
外模型也将在此阶段完成。
7．物理设计阶段：对于给定的基本数据模型选取一个最适合应用环境的物理结构的过程。
数据库的物理结构主要指数据库的存储记录格式、存储记录安排和存取方法。
8．数据库的实现：包括定义数据库结构、数据装载、编制与调试应用程序、数据库试运行。
二、ER模型的基本概念ER模型的基本元素是：实体、联系和属性。
2．实体：是一个数据对象，指应用中可以区别的客观存在的事物。
实体集：是指同一类实体构成的集合。
实体类型：是对实体集中实体的定义。
一般将实体、实体集、实体类型统称为实体。
3．联系：表示一个或多个实体之间的关联关系。
联系集：是指同一类联系构成的集合。
联系类型：是对联系集中联系的定义。
一般将联系、联系集、联系类型统称为联系。
4．同一个实体集内部实体之间的联系，称为一元联系；两个不同实体集实体之间的联系，称为二元联系，以此类推。
5．属性：实体的某一特性称为属性。
在一个实体中，能够惟一标识实体的属性或属性集称为实体标识符。
6． ER模型中，方框表示实体、菱形框表示联系、椭圆形框表示属性、实体与联系、实体与其属性、联系与其属性之间用直线连接。
实体标识符下画横线。
联系的类型要在直线上标注。
注意：联系也有可能存在属性，但联系本身没有标识符。
数据库系统教程课后答案(施伯乐)(第二版)
目录第1部分课程的教与学第2部分各章习题解答及自测题第1章数据库概论1.1 基本内容分析1.2 教材中习题1的解答1.3 自测题1.4 自测题答案第2章关系模型和关系运算理论2.1基本内容分析2.2 教材中习题2的解答2.3 自测题2.4 自测题答案第3章关系数据库语言SQL3.1基本内容分析3.2 教材中习题3的解答3.3 自测题3.4 自测题答案第4章关系数据库的规范化设计4.1基本内容分析4.2 教材中习题4的解答4.3 自测题4.4 自测题答案第5章数据库设计与ER模型5.1基本内容分析5.2 教材中习题5的解答5.3 自测题5.4 自测题答案第6章数据库的存储结构6.1基本内容分析6.2 教材中习题6的解答第7章系统实现技术7.1基本内容分析7.2 教材中习题7的解答7.3 自测题7.4 自测题答案第8章对象数据库系统8.1基本内容分析8.2 教材中习题8的解答8.3 自测题8.4 自测题答案第9章分布式数据库系统9.1基本内容分析9.2 教材中习题9的解答9.3 自测题9.4 自测题答案第10章中间件技术10.1基本内容分析10.2 教材中习题10的解答10.3 自测题及答案第11章数据库与WWW11.1基本内容分析11.2 教材中习题11的解答第12章 XML技术12.1基本内容分析12.2 教材中习题12的解答学习推荐书目1．国内出版的数据库教材（1）施伯乐,丁宝康,汪卫. 数据库系统教程(第2版). 北京:高等教育出版社,2003（2）丁宝康,董健全. 数据库实用教程(第2版). 北京:清华大学出版社,2003（3）施伯乐,丁宝康. 数据库技术. 北京:科学出版社,2002（4）王能斌. 数据库系统教程(上、下册). 北京:电子工业出版社,2002（5）闪四清. 数据库系统原理与应用教程. 北京:清华大学出版社,2001（6）萨师煊,王珊. 数据库系统概论(第3版). 北京:高等教育出版社,2000（7）庄成三,洪玫,杨秋辉. 数据库系统原理及其应用. 北京:电子工业出版社,20002．出版的国外数据库教材（中文版或影印版）（1）Silberschatz A，Korth H F，Sudarshan S. 数据库系统概念(第4版). 杨冬青,唐世渭等译. 北京:机械工业出版社,2003（2）Elmasri R A，Navathe S B. 数据库系统基础(第3版). 邵佩英,张坤龙等译. 北京:人民邮电出版社,2002（3）Lewis P M,Bernstein A,Kifer M. Databases and Transaction Processing:An Application-Oriented Approach, Addison-Wesley, 2002（影印版, 北京:高等教育出版社；中文版，施伯乐等译，即将由电子工业出版社出版）（4）Hoffer J A,Prescott M B,McFadden F R. Modern Database Management. 6th ed. Prentice Hall, 2002（中文版，施伯乐等译，即将由电子工业出版社出版）3．上机实习教材（1）廖疆星,张艳钗,肖金星. PowerBuilder 8.0 & SQL Server 2000数据库管理系统管理与实现. 北京:冶金工业出版社,2002（2）伍俊良. PowerBuilder课程设计与系统开发案例. 北京:清华大学出版社,20034．学习指导书（1）丁宝康,董健全,汪卫,曾宇昆. 数据库系统教程习题解答及上机指导. 北京:高等教育出版社,2003（2）丁宝康,张守志,严勇. 数据库技术学习指导书. 北京:科学出版社,2003（3）丁宝康,董健全,曾宇昆. 数据库实用教程习题解答. 北京:清华大学出版社,2003 （4）丁宝康. 数据库原理题典. 长春:吉林大学出版社,2002（5）丁宝康,陈坚,许建军,楼晓鸿. 数据库原理辅导与练习. 北京:经济科学出版社,2001第1部分课程的教与学1．课程性质与设置目的现在，数据库已是信息化社会中信息资源与开发利用的基础，因而数据库是计算机教育的一门重要课程，是高等院校计算机和信息类专业的一门专业基础课。
数据库课后答案 第二章(数据库系统基本原理)
《数据库技术及应用基础教程》第二章参考答案--责任人：袁圆、董婧灵、娄振霞一、选择题1~5：CDCCD 6~10：BDCCA 11~15：AD，ABCA 16：B二、填空题：1.数据库、数据库系统软件、数据库系统用户2. 关系名（属性名1，属性名2，属性名3,…）3.列4. 能标识独一实体的属性或属性组5.一张或几张表（或视图），结构，数据6. 使关系中的每一个属性为不可再分的单纯形域(消除“表中表”)，使关系中所有非主属性对任意一个侯选关键字不存在部分函数依赖（使关系中所有非主属性都完全函数依赖于任意一个侯选关键字），使关系中所有非主属性对任意一个侯选关键字不存在传递函数依赖7.需求分析阶段，概念结构设计阶段，逻辑结构设计阶段，数据库物理设计阶段，数据库实施阶段，数据库运行和维护阶段8.数据库应用系统（DBAS）9.安全性、完整性、并发控制和数据恢复10.发生故障后，故障前状态11.授权12.事务13.事务中包括的各个操作一旦开始执行，则一定要全部完成14.封锁，共享锁，排他锁15. 一致性，正确性16.系统自动完成三、简答题1、试述数据模型的概念、数据模型的作用和数据模型的三个要素。
答：数据模型是现实世界数据特征的一种抽象，一种表示实体类型及实体类型间联系的模型。
数据模型可以抽象、表示、处理现实中的数据和信息。
数据模型的三要素分别是：(1)数据结构：是所研究的对象类型的集合，是对系统静态特性的描述。
(2)数据操作：对数据库中各种对象(型)的实例(值)允许执行的操作的集合，操作及操作规则。
(3)数据的约束条件：是一组完整性规则的集合。
也就是说，对于具体的应用娄必须遵循特定的语义约束条件，以保证数据的正确、有效和相容。
2、试述网状、层次数据库的优缺点。
答：网状数据库的优点：（1）能更直接的描述现实世界；（2）具有良好的性能，存取效率更好。
网状数据库缺点：（1）结构复杂，应用系统越大数据库结构越复杂；（2）用法复杂，用户不易理解。
Oracle11g数据库基础教程-参考答案资料
SMON进程的主要功能包括：在实例启动时负责对数据库进行恢复；回收不再使用的临
时空间；将各个表空间的空闲碎片合并。
PMON进程的主要功能包括：负责恢复失败的用户进程或服务器进程，并且释放进程所
占用的资源； 清除非正常中断的用户进程留下的孤儿会话， 回退未提交的事务， 释放会话所
占用的锁、 SGA、 PGA 等资源；监控调度进程和服务器进程的状态，如果它们失败，则尝试
修改右侧对话框中
第 2 章 Oracle 数据库管理与开发工具
1．简答题
（1）
实现对 Oracle 运行环境的完全管理， 包括 Oracle 数据库、 Oracle 应用服务器、 HTTP 服务器等的管理；
实现对单个 Oracle 数据库的本地管理，包括系统监控、性能诊断与优化、 对象管理、存储管理、安全管理、作业管理、数据备份与恢复、数据移植等；
适合于工作组或部门级
的应用程序： 个人版数据库服务器只提供基本数据库管理功能和特性，
适合单用户的开发环
境，为用户提供开发测试平台。
（2）
常用数据库类型包括事务处理类、 数据仓库类以通用类型。 其中事务处理类型主要针对
具有大量并发用户连接， 并且用户主要执行简单事务处理的应用环境。 事务处理数据库的典 型应用有银行系统数据库、 Internet 电子商务数据库、证券交易系统数据库等。对于需要较 高的可用性和事务处理性能、 存在大量用户并行访问相同数据以及需要较高恢复性能的数据
Oracle 数据库物理结构包括数据文件、控制文件、重做日志文件、初始化参数文件、归 档文件、 口令文件等。 在控制文件中记录了当前数据库所有的数据文件的名称与位置、 日志文件的名称与位置，以及数据文件、重做日志文件的状态等。 （3）
(完整版)数据库系统基础教程第二章答案
(Lena, Hand,805-333, 12345),
(Lena, Hand,805-333, 23456)
Exercise 2.2.1c
For relation Accounts and the first tuple, the components are:
idNo
firstName
lastName
account
805-333
Lena
Hand
23456
805-333
Lena
Hand
12345
901-222
Robbie
Banks
12345
Exercise 2.2.2
Examples of attributes that are created for primarily serving as keys in a relation:
Vehicle Identification Numbers (VIN), a unique serial number used by the automotive industry to identify vehicles.
Exercise 2.2.3a
We can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36.
CREATE TABLE Outcomes (
ship CHAR(30), battle CHAR(30), result CHAR(10)
数据库系统教程（第三版课后答案）免费下载（可编辑）
数据库系统教程(第三版课后答案)免费下载第1章数据库概论1.1 基本内容分析本章的重要概念（1）DB、DBMS和DBS的定义（2）数据管理技术的发展阶段人工管理阶段、文件系统阶段、数据库系统阶段和高级数据库技术阶段等各阶段的特点。
（3）数据描述概念设计、逻辑设计和物理设计等各阶段中数据描述的术语，概念设计中实体间二元联系的描述（1:1，1:N，M:N）1.7 与“文件”结构相比，“数据库”结构有些什么不同？答：与文件结构相比，数据库结构主要有下面三点不同：数据的结构化。
文件由记录组成，但各文件之间缺乏联系。
数据库中数据在磁盘中仍以文件形式组织，但这些文件之间有着广泛的联系。
数据库的逻辑结构用数据模型来描述，整体结构化。
数据模型不仅描述数据本身的特点，还要描述数据之间的联系。
数据独立性。
文件只有设备独立性，而数据库还具有逻辑独立性和物理独立性。
访问数据的单位。
访问文件中的数据，以记录为单位。
访问数据库中的数据，以数据项（字段）为单位，增加了系统的灵活性。
1.8 什么是数据独立性？在数据库中有哪两级独立性？答：数据独立性是指应用程序与DB的数据结构之间相互独立。
在物理结构改变时，尽量不影响应用程序，称为物理数据独立性；在逻辑结构改变时，尽量不影响应用程序，称为逻辑数据独立性。
1.9 分布式数据库系统和面向对象数据库系统各有哪些特点？答：DDBS主要有三个特点：??数据物理上分布在各地，但逻辑上是一个整体；??每个场地既可以执行局部应用，也可以执行全局应用；??各地的计算机由数据通信网络相连接。
面向对象数据系统主要有两个特点：??面向对象数据模型能完整地描述现实世界的数据结构，能表达数据间嵌套、递归的联系。
??具有面向对象技术的封装性和继承性的特点，提高了软件的可重用性。
1.10 逻辑记录与物理记录，逻辑文件与物理文件有些什么联系和区别？答：逻辑数据是用户用以操作的数据形式，是抽象的概念化数据。
物理数据是实际存放在存储设备上的数据。
数据库基础第2版习题答案
数据库基础第2版习题答案数据库基础第2版习题答案数据库基础是计算机科学中非常重要的一门课程，它涵盖了数据库的基本原理、设计和应用。
在学习过程中，习题是帮助我们巩固所学知识的重要途径。
本文将为大家提供数据库基础第2版习题的答案，希望能对大家的学习有所帮助。
第一章数据库系统概述1. 什么是数据库系统？数据库系统是指由数据库、数据库管理系统（DBMS）和应用程序组成的一个整体。
它用于管理和组织大量的数据，并提供数据的存储、检索、更新和删除等功能。
2. 数据库系统的优点有哪些？数据库系统具有以下优点：- 数据共享：多个用户可以同时访问和共享数据库中的数据。
- 数据独立性：数据库系统能够将数据的逻辑表示与物理存储分离，使得应用程序与数据的具体存储方式无关。
- 数据一致性：数据库系统能够保证数据的一致性，即数据的完整性和正确性。
- 数据安全性：数据库系统提供了权限管理和数据备份等功能，保护数据的安全性和可靠性。
第二章关系数据库基本概念1. 什么是关系数据库？关系数据库是一种基于关系模型的数据库。
它使用表（表格）来组织和存储数据，表由行和列组成，每行表示一个记录，每列表示一个属性。
2. 什么是关系模型？关系模型是一种用于描述关系数据库的数据模型。
它使用关系（表）来表示实体和实体之间的关系，通过关系之间的连接来实现数据的查询和操作。
第三章关系数据库的完整性约束1. 什么是实体完整性约束？实体完整性约束是指关系数据库中的每个实体必须具有一个唯一的标识符（主键），且不能为空。
2. 什么是参照完整性约束？参照完整性约束是指关系数据库中的外键必须引用其他表中已存在的主键，保证数据的一致性和正确性。
第四章 SQL基本概念1. 什么是SQL？SQL（Structured Query Language）是一种用于管理和操作关系数据库的语言。
它包括数据查询语言（DQL）、数据定义语言（DDL）、数据控制语言（DCL）和数据操纵语言（DML）等部分。
数据库系统教程_课答案(施伯乐)(第三版)
第1章数据库概论1.1 基本内容分析1.1.1 本章的重要概念（1）DB、DBMS和DBS的定义（2）数据管理技术的发展阶段人工管理阶段、文件系统阶段、数据库系统阶段和高级数据库技术阶段等各阶段的特点。
（3）数据描述概念设计、逻辑设计和物理设计等各阶段中数据描述的术语，概念设计中实体间二元联系的描述（1:1，1:N，M:N）。
（4）数据模型数据模型的定义，两类数据模型，逻辑模型的形式定义，ER模型，层次模型、网状模型、关系模型和面向对象模型的数据结构以及联系的实现方式。
（5）DB的体系结构三级结构，两级映像，两级数据独立性，体系结构各个层次中记录的联系。
（6）DBMSDBMS的工作模式、主要功能和模块组成。
（7）DBSDBS的组成，DBA，DBS的全局结构，DBS结构的分类。
1.1.2本章的重点篇幅（1）教材P23的图1.24（四种逻辑数据模型的比较）。
（2）教材P25的图1.27（DB的体系结构）。
（3）教材P28的图1.29（DBMS的工作模式）。
（4）教材P33的图1.31（DBS的全局结构）。
1.2 教材中习题1的解答1.1 名词解释·逻辑数据：指程序员或用户用以操作的数据形式。
·物理数据：指存储设备上存储的数据。
·联系的元数：与一个联系有关的实体集个数，称为联系的元数。
·1:1联系：如果实体集E1中每个实体至多和实体集E2中的一个实体有联系，反之亦然，那么E1和E2的联系称为“1:1联系”。
·1:N联系：如果实体集E1中每个实体可以与实体集E2中任意个（零个或多个）实体有联系，而E2中每个实体至多和E1中一个实体有联系，那么E1和E2的联系是“1:N联系”。
·M:N联系：如果实体集E1中每个实体可以与实体集E2中任意个（零个或多个）实体有联系，反之亦然，那么E1和E2的联系称为“M:N联系”。
·数据模型：能表示实体类型及实体间联系的模型称为“数据模型”。
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Exercise 2.2.1aFor relation Accounts, the attributes are:acctNo, type, balanceFor relation Customers, the attributes are:firstName, lastName, idNo, accountExercise 2.2.1bFor relation Accounts, the tuples are:(12345, savings, 12000),(23456, checking, 1000),(34567, savings, 25)For relation Customers, the tuples are:(Robbie, Banks, 901-222, 12345),(Lena, Hand, 805-333, 12345),(Lena, Hand, 805-333, 23456)Exercise 2.2.1cFor relation Accounts and the first tuple, the components are: 123456 → acctNosavings → type12000 → balanceFor relation Customers and the first tuple, the components are: Robbie → firstNameBanks → lastName901-222 → idNo12345 → accountExercise 2.2.1dFor relation Accounts, a relation schema is:Accounts(acctNo, type, balance)For relation Customers, a relation schema is:Customers(firstName, lastName, idNo, account) Exercise 2.2.1eAn example database schema is:Accounts (acctNo,type,balance)Customers (firstName,lastName,idNo,account)Exercise 2.2.1fA suitable domain for each attribute:acctNo → Integertype → Stringbalance → IntegerfirstName → StringlastName → StringidNo → String (because there is a hyphen we cannot use Integer)account → IntegerExercise 2.2.1gAnother equivalent way to present the Account relation:Another equivalent way to present the Customers relation:Exercise 2.2.2Examples of attributes that are created for primarily serving as keys in a relation:Universal Product Code (UPC) used widely in United States and Canada to track products in stores.Serial Numbers on a wide variety of products to allow the manufacturer to individually track each product.Vehicle Identification Numbers (VIN), a unique serial number used by the automotive industry to identify vehicles.Exercise 2.2.3aWe can order the three tuples in any of 3! = 6 ways. Also, the columns can be ordered in any of 3! = 6 ways. Thus, the number of presentations is 6*6 = 36. Exercise 2.2.3bWe can order the three tuples in any of 5! = 120 ways. Also, the columns can be ordered in any of 4! = 24 ways. Thus, the number of presentations is120*24 = 2880Exercise 2.2.3cWe can order the three tuples in any of m! ways. Also, the columns can be ordered in any of n! ways. Thus, the number of presentations is n!m!Exercise 2.3.1aCREATE TABLE Product (maker CHAR(30),model CHAR(10) PRIMARY KEY,type CHAR(15));Exercise 2.3.1bCREATE TABLE PC (model CHAR(30),speed DECIMAL(4,2),ram INTEGER,hd INTEGER,price DECIMAL(7,2));Exercise 2.3.1cCREATE TABLE Laptop (model CHAR(30),speed DECIMAL(4,2),ram INTEGER,hd INTEGER,screen DECIMAL(3,1),price DECIMAL(7,2));Exercise 2.3.1dCREATE TABLE Printer (model CHAR(30),color BOOLEAN,type CHAR (10),price DECIMAL(7,2));Exercise 2.3.1eALTER TABLE Printer DROP color;Exercise 2.3.1fALTER TABLE Laptop ADD od CHAR (10) DEFAULT ‘none’; Exercise 2.3.2aCREATE TABLE Classes (class CHAR(20),type CHAR(5),country CHAR(20),numGuns INTEGER,bore DECIMAL(3,1),displacement INTEGER);Exercise 2.3.2bCREATE TABLE Ships (name CHAR(30),class CHAR(20),launched INTEGER);Exercise 2.3.2cCREATE TABLE Battles (name CHAR(30),date DATE);Exercise 2.3.2dCREATE TABLE Outcomes (ship CHAR(30),battle CHAR(30),result CHAR(10));Exercise 2.3.2eALTER TABLE Classes DROP bore;Exercise 2.3.2fALTER TABLE Ships ADD yard CHAR(30);Exercise 2.4.1aR1 := σspeed ≥ 3.00 (PC)R2 := πmodel(R1)model100510061013Exercise 2.4.1bR1 := σhd ≥ 100 (Laptop)R2 := Product (R1)R3 := πmaker (R2)makerEABFGExercise 2.4.1cR1 := σmaker=B (Product PC)R2 := σmaker=B (Product Laptop)R3 := σmaker=B (Product Printer)R4 := πmodel,price (R1)R5 := πmodel,price (R2)R6: = πmodel,price (R3)R7 := R4 R5 R6model price1004 6491005 6301006 10492007 1429Exercise 2.4.1dR1 := σcolor = true AND type = laser (Printer)R2 := πmodel (R1)model30033007Exercise 2.4.1eR1 := σtype=laptop (Product)R2 := σtype=PC(Product)R3 := πmaker(R1)R4 := πmaker(R2)R5 := R3 – R4makerFGExercise 2.4.1fR1 := ρPC1(PC)R2 := ρPC2(PC)R3 := R1 (PC1.hd = PC2.hd AND PC1.model <> PC2.model) R2R4 := πhd(R3)hd25080160Exercise 2.4.1gR1 := ρPC1(PC)R2 := ρPC2(PC)R3 := R1 (PC1.speed = PC2.speed AND PC1.ram = PC2.ram AND PC1.model < PC2.model) R2R4 := πPC1.model,PC2.model(R3)PC1.model PC2.model1004 1012Exercise 2.4.1hR1 := πmodel(σspeed ≥ 2.80(PC)) πmodel(σspeed ≥ 2.80(Laptop))R2 := πmaker,model(R1 Product)R3 := ρR3(maker2,model2)(R2)R4 := R2 (maker = maker2 AND model <> model2) R3R5 := πmaker(R4)makerBEExercise 2.4.1iR1 := πmodel,speed(PC)R2 := πmodel,speed(Laptop)R3 := R1 R2R4 := ρR4(model2,speed2)(R3)R5 := πmodel,speed (R3 (speed < speed2 ) R4)R6 := R3 – R5R7 := πmaker(R6 Product)makerBExercise 2.4.1jR1 := πmaker,speed(Product PC)R2 := ρR2(maker2,speed2)(R1)R3 := ρR3(maker3,speed3)(R1)R4 := R1 (maker = maker2 AND speed <> speed2) R2R5 := R4 (maker3 = maker AND speed3 <> speed2 AND speed3 <> speed) R3R6 := πmaker(R5)makerADEExercise 2.4.1kR1 := πmaker,model(Product PC)R2 := ρR2(maker2,model2)(R1)R3 := ρR3(maker3,model3)(R1)R4 := ρR4(maker4,model4)(R1)R5 := R1 (maker = maker2 AND model <> model2) R2R6 := R3 (maker3 = maker AND model3 <> model2 AND model3 <> model) R5R7 := R4 (maker4 = maker AND (model4=model OR model4=model2 OR model4=model3)) R6R8 := πmaker(R7)makerABDEExercise 2.4.2aπmodelσspeed≥3.00PCExercise 2.4.2bLaptopσhd ≥ 100 ProductmakerExercise 2.4.2cσmaker=B πmodel,price σmaker=B πmodel,price σmaker=B πmodel,priceProduct PC Laptop Printer ProductProductExercise 2.4.2d Printerσcolor = true AND type = laserπmodelExercise 2.4.2eσtype=laptopσtype=PC πmakerπmaker ProductProductExercise 2.4.2fρPC1ρPC2 (PC1.hd = PC2.hd AND PC1.model <> PC2.model)πhdPC PCExercise 2.4.2gρPC1ρPC2PC PC(PC1.speed = PC2.speed AND PC1.ram = PC2.ram AND PC1.model < PC2.model)πPC1.model,PC2.modelExercise 2.4.2hPC Laptop σspeed ≥ 2.80σspeed ≥ 2.80πmodelπmodel Productπmaker,modelρR3(maker2,model2)(maker = maker2 AND model <> model2)makerExercise 2.4.2iPCLaptopProductπmodel,speed πmodel,speed ρR4(model2,speed2)πmodel,speed(speed < speed2 )–makerExercise 2.4.2jProduct PC πmaker,speed ρR3(maker3,speed3)ρR2(maker2,speed2)(maker = maker2 AND speed <> speed2)(maker3 = maker AND speed3 <> speed2 AND speed3 <> speed)makerExercise 2.4.2kπmaker(maker4 = maker AND (model4=model OR model4=model2 OR model4=model3)) (maker3 = maker AND model3 <> model2 AND model3 <> model)(maker = maker2 AND model <> model2)ρR2(maker2,model2)ρR3(maker3,model3)ρR4(maker4,model4)πmaker,modelProduct PCExercise 2.4.3aR1 := σbore ≥ 16 (Classes)R2 := πclass,country (R1)Exercise 2.4.3bR1 := σlaunched < 1921 (Ships)R2 := πname (R1)RamilliesRenownRepulseResolutionRevengeRoyal OakRoyal SovereignTennesseeExercise 2.4.3cR1 := σbattle=Denmark Strait AND result=sunk(Outcomes)R2 := πship (R1)shipBismarckHoodExercise 2.4.3dR1 := Classes ShipsR2 := σlaunched > 1921 AND displacement > 35000 (R1)R3 := πname (R2)nameIowaMissouriMusashiNew JerseyNorth CarolinaWashingtonWisconsinYamatoExercise 2.4.3eR1 := σbattle=Guadalcanal(Outcomes)R2 := Ships (ship=name) R1R3 := Classes R2R4 := πname,displacement,numGuns(R3)name displacement numGuns Kirishima 32000 8Washington 37000 9Exercise 2.4.3fR1 := πname(Ships)R2 := πship(Outcomes)R3 := ρR3(name)(R2)R4 := R1 R3nameCaliforniaHarunaHieiIowaKirishimaKongoMissouriMusashiNew JerseyNorth CarolinaRamilliesRenownRepulseResolutionRevengeRoyal OakRoyal SovereignTennesseeWashingtonExercise 2.4.3gFrom 2.3.2, assuming that every class has one ship named after the class.R1 := πclass (Classes) R2 := πclass (σname <> class (Ships)) R3 := R1 – R2Exercise 2.4.3hR1 := πcountry (σtype=bb (Classes))R2 := πcountry (σtype=bc (Classes))R3 := R1 ∩ R2Exercise 2.4.3iR1 := πship,result,date (Battles (battle=name) Outcomes)R2 := ρR2(ship2,result2,date2)(R1)R3 := R1 (ship=ship2 AND result=damaged AND date < date2) R2R4 := πship (R3)No results from sample data.Exercise 2.4.4aσbore ≥ 16πclass,country ClassesExercise 2.4.4bσlaunched < 1921πname ShipsExercise 2.4.4cWisconsin Yamato Arizona Bismarck Duke of York Fuso Hood King George V Prince of Wales Rodney Scharnhorst South Dakota West Virginia Yamashiro class Bismarck countryJapan Gt. BritainOutcomesπshipσbattle=Denmark Strait AND result=sunkExercise 2.4.4dClasses Ships σlaunched > 1921 AND displacement > 35000πnameExercise 2.4.4e σbattle=Guadalcanal Outcomes ShipsClasses(ship=name)πname,displacement,numGunsExercise 2.4.4fShipsOutcomesπnameπship ρR3(name)Exercise 2.4.4g ClassesShips πclass σname <> class πclass –Exercise 2.4.4hClasses Classesσtype=bb σtype=bcπcountry πcountry∩Exercise 2.4.4iπship(ship=ship2 AND result=damaged AND date < date2)ρR2(ship2,result2,date2)πship,result,date(battle=name)Battles OutcomesExercise 2.4.5The result of the natural join has only one attribute from each pair of equated attributes. On the other hand, the result of the theta-join has both columns of the attributes and their values are identical.Exercise 2.4.6UnionIf we add a tuple to the arguments of the union operator, we will get all of the tuples of the original result and maybe the added tuple. If theadded tuple is a duplicate tuple, then the set behavior will eliminate that tuple. Thus the union operator is monotone.IntersectionIf we add a tuple to the arguments of the intersection operator, we will get all of the tuples of the original result and maybe the added tuple. If the added tuple does not exist in the relation that it is added but does exist in the other relation, then the result set will include the added tuple.Thus the intersection operator is monotone.DifferenceIf we add a tuple to the arguments of the difference operator, we may not get all of the tuples of the original result. Suppose we have relations R and S and we are computing R – S. Suppose also that tuple t is in R but not in S. The result of R – S would include tuple t. However, if we add tuple t to S, then the new result will not have tuple t. Thus the difference operator is not monotone.ProjectionIf we add a tuple to the arguments of the projection operator, we will get all of the tuples of the original result and the projection of the added tuple. The projection operator only selects columns from the relation and does not affect the rows that are selected. Thus the projection operator is monotone.SelectionIf we add a tuple to the arguments of the selection operator, we will get all of the tuples of the original result and maybe the added tuple. If the added tuple satisfies the select condition, then it will be added to the new result. The original tuples are included in the new result because they still satisfy the select condition. Thus the selection operator is monotone.Cartesian ProductIf we add a tuple to the arguments of the Cartesian product operator, we will get all of the tuples of the original result and possibly additional tuples. The Cartesian product pairs the tuples of one relation with the tuples of another relation. Suppose that we are calculating R x S where R has m tuples and S has n tuples. If we add a tuple to R that is not already in R, then we expect the result of R x S to have (m + 1) * n tuples.Thus the Cartesian product operator is monotone.Natural JoinsIf we add a tuple to the arguments of a natural join operator, we will get all of the tuples of the original result and possibly additional tuples.The new tuple can only create additional successful joins, not less. If, however, the added tuple cannot successfully join with any of theexisting tuples, then we will have zero additional successful joins. Thus the natural join operator is monotone.Theta JoinsIf we add a tuple to the arguments of a theta join operator, we will get all of the tuples of the original result and possibly additional tuples. The theta join can be modeled by a Cartesian product followed by a selection on some condition. The new tuple can only create additional tuples in the result, not less. If, however, the added tuple does not satisfy the select condition, then no additional tuples will be added to the result. Thus the theta join operator is monotone.RenamingIf we add a tuple to the arguments of a renaming operator, we will get all of the tuples of the original result and the added tuple. The renaming operator does not have any effect on whether a tuple is selected or not. In fact, the renaming operator will always return as many tuples as its argument. Thus the renaming operator is monotone.Exercise 2.4.7aIf all the tuples of R and S are different, then the union has n + m tuples, and this number is the maximum possible.The minimum number of tuples that can appear in the result occurs if every tuple of one relation also appears in the other. Then the union has max(m , n) tuples.Exercise 2.4.7bIf all the tuples in one relation can pair successfully with all the tuples in the other relation, then the natural join has n * m tuples. This number would be the maximum possible.The minimum number of tuples that can appear in the result occurs if none of the tuples of one relation can pair successfully with all the tuples in the other relation. Then the natural join has zero tuples.Exercise 2.4.7cIf the condition C brings back all the tuples of R, then the cross product will contain n * m tuples. This number would be the maximum possible.The minimum number of tuples that can appear in the result occurs if the condition C brings back none of the tuples of R. Then the cross product has zero tuples.Exercise 2.4.7dAssuming that the list of attributes L makes the resulting relation πL(R) and relation S schema compatible, then the maximum possible tuples is n. This happens when all of the tuples of πL(R) are not in S.The minimum number of tuples that can appear in the result occurs when all of the tuples in πL(R) appear in S. Then the difference has max(n–m , 0) tuples.Exercise 2.4.8Defining r as the schema of R and s as the schema of S:1.πr(R S)2.R δ(πr∩s(S)) where δ is the duplicate-elimination operator in Section 5.2 pg. 2133.R – (R –πr(R S))Exercise 2.4.9Defining r as the schema of R1.R - πr(R S)Exercise 2.4.10πA1,A2…An(R S)Exercise 2.5.1aσspeed < 2.00 AND price > 500(PC) = øModel 1011 violates this constraint.Exercise 2.5.1bσscreen < 15.4 AND hd < 100 AND price ≥ 1000(Laptop) = øModel 2004 violates the constraint.Exercise 2.5.1cπmaker(σtype = laptop(Product)) ∩ πmaker(σtype = pc(Product)) = øManufacturers A,B,E violate the constraint.Exercise 2.5.1dThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R4 that stand for nodes of expression trees. Here is the sequence:R1(maker, model, speed) := πmaker,model,speed(Product PC)R2(maker, speed) := πmaker,speed(Product Laptop)R3(model) := πmodel(R1 R1.maker = R2.maker AND R1.speed ≤ R2.speed R2)R4(model) := πmodel(PC)The constraint is R4 ⊆ R3Manufacturers B,C,D violate the constraint.Exercise 2.5.1eπmodel(σLaptop.ram > PC.ram AND Laptop.price ≤ PC.price(PC × Laptop)) = øModels 2002,2006,2008 violate the constraint.Exercise 2.5.2aπclass(σbore > 16(Classes)) = øThe Yamato class violates the constraint.Exercise 2.5.2bπclass(σnumGuns > 9 AND bore > 14(Classes)) = øNo violations to the constraint.Exercise 2.5.2cThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R5 that stand for nodes of expression trees. Here is the sequence:R1(class,name) := πclass,name(Classes Ships)R2(class2,name2) := ρR2(class2,name2)(R1)R3(class3,name3) := ρR3(class3,name3)(R1)R4(class,name,class2,name2) := R1 (class = class2 AND name <> name2) R2R5(class,name,class2,name2,class3,name3) := R4 (class=class3 AND name <> name3 AND name2 <> name3) R3The constraint is R5 = øThe Kongo, Iowa and Revenge classes violate the constraint.Exercise 2.5.2dπcountry(σtype = bb(Classes)) ∩ πcountry(σtype = bc(Classes)) = øJapan and Gt. Britain violate the constraint.Exercise 2.5.2eThis complex expression is best seen as a sequence of steps in which we define temporary relations R1 through R5 that stand for nodes of expression trees. Here is the sequence:R1(ship,battle,result,class) := πship,battle,result,class(Outcomes (ship = name) Ships)R2(ship,battle,result,numGuns) := πship,battle,result,numGuns(R1 Classes)R3(ship,battle) := πship,battle(σnumGuns < 9 AND result = sunk (R2))R4(ship2,battle2) := ρR4(ship2,battle2)(πship,battle(σnumGuns > 9(R2)))R5(ship2) := πship2(R3 (battle = battle2) R4)The constraint is R5 = øNo violations to the constraint. Since there are some ships in the Outcomes table that are not in the Ships table, we are unable to determine the number of guns on that ship.Exercise 2.5.3Defining r as the schema A1,A2,…,A n and s as the schema B1,B2,…,B n:πr(R) πs(S) = øwhere is the antisemijoinExercise 2.5.4The form of a constraint as E1 = E2 can be expressed as the other two constraints.Using the “equating an expression to the empty set” method, we can simply say:E1– E2 = øAs a containment, we can simply say:E1⊆ E2 AND E2⊆ E1Thus, the form E1 = E2 of a constraint cannot express more than the two other forms discussed in this section.。