计算机英语(第三版)作者：刘兆毓、郑家农(普通高等教育“十一五”国家级规划教材).ppt.ppt

PART Ⅱ COMPUTER SOFTWARE
CHAPTER 3 MATHEMATIC FUNDAMENTALS
3.1 BOOLEAN ALGEBRA
3.1 BOOLEAN ALGEBRAMain poin Nhomakorabea:●
Development and function of boolean algebra Concept of set algebra Set operations Boolean operations
让步状语从句
A Boolean algebra is a finite or infinite set of elements together with three operations—negation, addition, and multiplication—that correspond to the set operations of complementation, union, and intersection,
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计算机英语（第三版）
The concept of a Boolean algebra was first proposed by the English mathematician George Boole in 1847. Since that time, Boole’s original conception has been extensively developed and refined by algebraists and
计算机英语（第三版）
The most intuitive development of boolean algebras
arises from the concept of a set algebra. Let S ={a,b,c}
and T={a,b,c,d,e} be two sets consisting of three and five elements, respectively. We say that S is a subset of T, since every element of S (namely, a, b, and c) belongs to T. Since T has five elements, there are 25 subsets of T,
intersection
While other set operations may be defined［6］, the operations of complementation, union, and intersection are of primary interest to us .
计算机英语（第三版）
宾语补足语 定语从句
has as its complement (with respect to T) S={d,e}.The union
of any two sets (subsets of a given set) consists of those
elements that are in one or the other or in both given sets
［5 ］;
定语从句
that are in both given sets.
计算机英语（第三版）
定语从句
the intersection of two sets consists of those elements
We use the symbol ∪ to denote the union, and ∩ to denote the intersection of two sets. For example, if B={b,d,e}, then B∪S={a,b,c,d,e}, and B∩S={b}. ?2 ● Explain the operations of union and
原因状语从句
for we may choose any individual element to be included
or omitted from a subset［2］.Note that these 32 subsets include T itself and the empty set, which contains no elements at all［3］.
计算机英语（第三版）
原因状语从句
If T contains all elements of concern, it is called the
universal set. Given a subset of T, such as S,we may define the complement of S with respect to a universal set T to consist of precisely those elements of T which are not included in the given subset［4］. Thus, S as above defined
定语从句 同位语
respectively.Among the elements of a Boolean algebra are
two distinguished elements:0, corresponding to the empty set;and 1,corresponding to the universal set. For any given element of a Boolean algebra,there is a unique complement with the property that a+a=1 and aa=0.
logicians［1］. The relationships among Boolean algebra,
set algebra, logic, and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers. ?1 ● What is the fundamentals of electronic digital computers ?