逻辑关联词1-P
逻辑关联词汇总
常见的上下文（句）逻辑关系:(部分常用标志词和短语)并列关系and, and also, or, neither……nor, either……or, not only……but also,likewise(同样地，也), similarly（同样，类似于）,equally（同样地，相等的）, in the same way, that is to say, as well as, the same……as;递进关系also, then, besides, additionally\in addition（此外，加之）, furthermore\moreover（而且，此外）,what is more(而且); indeed（甚至，的确）;因果关系because, for, since, as,due to, thanks to（由于，幸亏）, on account of, because of, considering that, seeing that（鉴于由于）,in that, now that（既然，由于）, lest（唯恐，以免）,thus, hence（因此，今后）, therefore, so, so…..that, such…..that, in order that, consequently（因此，结果）, accordingly（因此，于是）,as a result（结果）, for this reason(因此，由于这个原因);转折关系but, however, yet, contrarily（相反，反之）, on the contrary（正相反）, by contrast（相比之下）,on the other hand, unfortunately;让步关系Although\though(虽然), even though\even if(即使), even（甚至，即使）, nevertheless（然而，不过）,Despite\ in spite of(尽管); regardless of（不顾，不管）;Anyway\ anyhow (无论如何，不管怎样)列举（顺序）关系first\second\last of all, in the first place\in the second place\finally, to begin with\ to continue, first……then,on one hand……on the other hand, for one thing……for another, one……another, some……others……still others;对比关系while, whereas（然而，鉴于）, as, / rather than, instead of（代替，不是…而是）, not….. but;时间关系when, whenever, before, after, since, as, while, until, till,simultaneously（同时地）, meanwhile（同时，其间）, in the meantime（在此期间，于此际）, at the same time;条件关系if, only if, if only, unless, otherwise（否则）, as soon as, as long as, in case, supposethat\supposing that(假如),provided that\ providing that（倘若，假如）, when, whenever, with(随着);举例关系such as, for example, for instance, of (these, those, them), among (these, those, them), to illustrate（举例）,as an illustration（作为例证）, to take an example , namely，more specifically speaking（更具体的来说）。
十大逻辑关系关联词总结
完型文章中常见的上下文（句）逻辑关系& 部分常用标志词和短语and also, or, neither……nor, either……or, not only……but also, likewise, similarly,& 部分常用标志词和短语then, besides, additionally, in addition, furthermore, moreover, what is more;& 部分常用标志词和短语order that, consequently, accordingly, due to, thanks to, in response to, on account of, because of, considering that, seeing that, in that, now that, lest, as a result,& 部分常用标志词和短语& 部分常用标志词和短语regardless of;& 部分常用标志词和短语with\ to continue, first……then, on one hand……on the other hand, for one& 部分常用标志词和短语& 部分常用标志词和短语whenever, before, after, since, as, while, until, till, simultaneously,& 部分常用标志词和短语& 部分常用标志词和短语them), to illustrate, as an illustration, to take an example, more specifically speaking, namely;关联词运用实例说明1a case in point, after all, as a proof, as an illustration, as an example, for example, for instance, in particular, just as, namely, such, specifically, that is, to illustrate, to demonstratea) Many southern cities are growing above the national average — Atlanta is a case in point.b) The news about calcium and kidney stones is a case in point.c) Prisoners should be treated with respect — they are human beings after all.d) These are, after all, very familiar species.e) It's extremely expensive to live in New York. For example, I pay $1, 250 for a one-bedroom apartment.f) Many countries, for example Mexico and Japan, have a lot of earthquakes.g) Old English was in many ways similar to Modern German. For instance, the nouns, adjectives, and verbs were highly inflected.h) We need to rethink the way we consume energy. Take, for instance, our approach to transport.i) Automobile prices in particular have fallen in recent months.j) His last album sold half a million copies and we hope this one will be just as (=equally) popular.k) One of the most important stages has yet to be started, namely beginning to fit the person into their new job.1) The issues are in two main clusters, namely the safety and the pricing and procurement of drugs.m) The rules make it quite clear what should be done in such a situation.n) We're talking about money —specifically, the money we need to repair our schools.o) One solution would be to change the shape of the screen, that is, to make it wider.2additionally, again, along with, also, and, and then, as well as, besides, equally, even, further, furthermore, in addition, in other words, just as, likewise, moreover, not only...but also, similarly, to put it another way, to repeat, then, too, what's morea) They may also additionally represent much more; they may indeed have a highly integrating social function.b) And again, these workshops will benefit the community considerably.c) Dunne was murdered, along with three guards.d) Sugar is bad for your teeth. It can also contribute to heart disease.e) This is a flexible and user-friendly system suitable for beginners and advanced users alike.f) Fry the onions gently, and then add the meat and cook for a few minutes.g) The organization gives help and support to people in need, as well as raising money for local charities.h) People choose jobs for other reasons besides money.i) We want the economy to grow, but equally we want low inflation.j) It is possible to make good movies cheaply. Further, "low-budget" doesn't have to mean "bad. "k) The majority of Americans increased their wealth in the past decade. Furthermore, the gains were substantial.l) A new security system was installed. In addition, extra guards were hired.m) The company provides cheap Internet access. In addition, it makes shareware freely available.n) The tax only affects people on incomes over $200, 000—in other words, the very rich.o) The clams were delicious. Likewise, the eggplant was excellent.p) Using language is a very complex enterprise. Moreover, there is more to communication than merely putting sentences together.q) The system was not only complicated but also ineffective.r) The cost of food and clothing has come down in recent years. Similarly, fuel prices have fallen quite considerably.s) Money makes money. To put it another way, the more you invest, the greater your potential profit will be.t) The problem demands a global solution. To put it another way, local regulations will have very little effect.u) First you need to collect all the information and make detailed notes. Then you can start to actually write your essay.v) Think about what you owe, too, in terms of mortgages, credit cards, loans or hire purchase.w) Gas is a very efficient fuel. And what' s more, it's clean.3above all, anyway, as a matter of fact, certainly, indeed, in fact, in particular, most important, obviously, of course, surely, to be sure, truly, undoubtedly, without doubta) Although it is somewhat limited in its applications it is easy to operate and above all it is fun.b) He got lost and spent hours looking for the station, and anyway it was past midnight by the time he got home.c) And, as a matter of fact, the U. S. Golf Association was delighted.d) Books and people certainly affected him.e) Most of the essays were very good indeed.f) Her teachers said she was a slow learner, whereas in fact she was partially deaf.g) Automobile prices in particular have fallen in recent months.h) But the reverse is true when an attorney represents a person who is obviously guilty or whose guilt is widely perceived.i) This is very obviously the approach of some one writing exclusively and specifically for the young.j) Of course there will be some difficult times ahead.k) If a sign were needed that the Internet has become a real market, the arrival of tax avoidance is surely it.l) Throwing money at the problem is surely not the way to convince people of sincerity.m) It was difficult, to be sure, but somehow we managed to finish the job.n) If we truly believe we can win, then we have a very good chance at doing it.o) Undoubtedly, public interest in folk music has declined.p) Sally was without doubt one of the finest swimmers in the school.10and, besides, finally, first, firstly, further, in the first place, last, next, second, secondly, third, thirdly, to begin with, to start with,a) It also assigned staff people to work with individual companies that wanted to launch a program.b) This is a flexible and user-friendly system suitable for beginners and advanced users alike.c) You need to know what tights you have and how to use them.d) Besides going to aerobics twice a week, she tides horses on Saturdays.e) And finally, I' d like to thank the crew.f) First, I'd like to thank everyone for coming.g) The application of the five stages to the task illustrated would involve, firstly, the definition of the task.h) It is possible to make good movies cheaply. Further, "low-budget" doesn't have to mean "bad. "i) And there i. s the question of the relevance of the trading of information in the first place.j) Connect the red wires first and the black ones last.k) First you need to select the text you want to move. Next, click on the "Move" command at the top of the screen.l) But, second, in the vast majority of markets, efficient production can be attained with a high degree of competition.m) The more you practise the better you will become at selecting historical information to suit firstly your essay and secondly your argument.n) To begin with, much of this new housing is not affordable.o) I' m not going to Vegas. To start with, I don' t like gambling, and I also can' t get time off work.34by contrast, but, conversely, in contrast, instead, on the contrary, on the other hand, otherwise, unlike, whereas, while, yeta) The birth rate for older women has declined, but, by contrast, births to teenage mothers have increased.b) The purpose of the scheme is not to help the employers but to provide work for young people.c) American consumers prefer white eggs; conversely, British buyers like brown eggs.d) Scandinavian cruises are very popular in the summer; conversely, the Carib bean is most popular in the winter.e) The stock lost 60 cents a share, in contrast to last year, when it gained 21 cents.f) Instead of being annoyed, he seemed quite pleased.g) It wasn't a good thing; on the contrary it was a huge mistake.h) Nuclear power is relatively cheap. On the other hand, you could argue that it's not safe.i) It is equally vital that both should be mentioned, otherwise a client, particularly a buyer, could be seriously misled.j) Unlike most people in the office, I don't come to work by car.k) A bowl of instant oatmeal costs about $1. 5, whereas regular oatmeal costs only $0. 5 per bowl.l) The old system was fairly complicated whereas the new system is really very simple.m) Schools in the north tend to be better equipped, while those in the south are relatively poor.n) Last summer there was a drought, yet some people were still watering their5by comparison, equally, equally important, in comparison, in the same way, in the same manner, like, likewise, similarlya) After months of living in a tropical climate, Spain seemed cool by comparison.b) By comparison with other European countries, car prices in the UK are very high.c) Even when the correct word was given a high probability, there were many other words with an equally high probability.d) Many business people do not know what sexual harassment is. Equally important, they do not know how to prevent it.e) an extremely unpleasant disease which is, however, easy to treatf) Cotton production was on the increase. However, it was still a small industry compared to hemp and canvas production.g) The deaf children of hearing parents are almost normal in comparison, having everything except language experience.h) There is often stronger social control evident in the socialisation of girls in comparison to boys.i) Good management accounts separate the well-organised from the rest but are not vital in the same way.j) I don't want him treating me like Jim treated me.k) The clams were delicious. Likewise, the eggplant was excellent.l) The cost of food and clothing has come down in recent years. Similarly, fuel6admittedly, after all, all the same, although, certainly, clearly, even so, it is true (that), in spite of, nevertheless, of course, still, truea) The technique is painful, admittedly, but it benefits the patient greatly.b) Printing and presentation should be as attractive as possible — after all the library is an attractive place, isn't it?c) I realise she can be very annoying, but I think you should apologise all thesame.d) We decided to take rooms in Longwood House, although we knew we could not really afford the rent.e) We are not especially well-treated, certainly not as well as the locals.f) Clearly, the racial problems in America have no easy answers.g) The fines for speeding are large, but even so, they are not always a deterrent.h) And it is true that after his death she ceased to exist for the world beyond the farm.i) But in spite of the hardships, real efforts and progress are being made.j) A false belief may nevertheless be justified.k) Though employment growth is down, the area is still attracting health care, 8although, but, despite, except for, though, however, in spite of, instead, nevertheless, on the other hand, otherwise, rather than, though, yeta) You can copy down my answers, although I'm not sure if they're right.b) In the US it is normal for the police to carry guns, but not in Britain.c) Despite international pressure, progress has slowed in the peace talks.d) Pen Pros: Except for personal letters, handwritten notes are withering into extinction.e) The rooms, though small, were pleasant and airy.f) This is a cheap and simple process. However there are dangers.g) In spite of her success, Spencer continues to get depressed.h) Cardew did not join the navy. Instead, he decided to join the theater and become an actor.i) Thus we can talk of a local government system which is different from a central government system but nevertheless interacts with it.j) Reintroduction of food after elemental regimens must nevertheless be undertaken with the greatest of care irrespective of whether or not elimination diets are used.k) The hamburger was tough and overcooked. The fries, on the other hand, were terrific, and well worth the money.l) Stir the sauce until it cools, otherwise it will be lumpy.m) It presumes that reality is dynamic rather than static, and therefore seeks relationships between ideas, to aim at synthesis.n) There is no important theory-based reason why these countries rather than others were selected.o) The offenders were dealt with firmly though fairly.p) They charge incredibly high prices, yet customers keep coming back for 7accordingly, as a result, consequently, for this reason, hence, in this way, so, therefore, thusa) Some of the laws were contradictory. Accordingly, measures were taken to clarify them.b) As many as 2, 500 people died as a result of the earthquake and the ensuing tidal waves.c) Most computer users have never received any formal keyboard training. Consequently, their keyboard skills are inefficient.d) The cost of transport is a major expense for an industry. Hence factory location is an important consideration.e) In this way normal healthy people may be tested without inducing any damage in their brain.f) The building work is taking quite a long time, and therefore costing us money.g) Most of the evidence was destroyed in the fire. Thus it would be almost 9as has been noted(mentioned，stated)，at last，finally，in a word，all in all，in brief, in conclusion, in short，in sum，in summary，to conclude，to sum up，to summarizea)An inhibition，as mentioned above，is rarely used．b)At last, we were able to afford a house．c)We finally found a decent apartment close to campus．d)Pop，in a word，is fascination versus meaning．e)It was，all in all，more like a prison than an office．f)In brief，the President plarts to cut defense spellding and lowet taxes.g)In conclusion，I want to thank all the people who have volunteered their time to our organization．h)In short，the report says that more money should be spent on education.i)In sum，we need to cut costs．j) In summary, do not sell your shares.k) To conclude, the prospects for philosophy of religion look brighter than they have done for many moons.l) To sum up, for a healthy heart you must take regular exercise and stop smoking. rn) To summarize, in most cases the schools were achieving the standards set.。
作文常用逻辑关联词
1 •表递进，强调besides）：除了，此外，而且（句首常用，句中，句尾均可）e.g. The house was out of our price range and too big anyway. Besides, I'd grownfond of our li卄le rented house.（反正这个房子超出了我们的预算范围，而且也太大了。
再说，我已经渐渐卑欢上我们租的小房子了）You get to sample lots of baked things and take home masses of cookies besides/你可以品尝许多烘烤食品，此外还能带许多饼干回家）11hink she has many good qualities besides being very beautiful.（我觉得她除了非常漂亮之外，还有许多好的品质）kdditionally|：另外（句首常用）e.g. All teachers are qualified to teach their native language. Additionally, weselect our teachers for their engaging personalities.（所有教0帀都具备教授其母语的资格。
另外，我们还根据富有魅力的个性来选择我们的教师）furthermore：此外，而且（句首常用）e.g.Furthermore, they claim that any such interference is completely ineffective.（此外，他们声称任何此类干涉都是完全无效的）moreover：此外，而且（句首常用，较正式）e.g. She saw that there was indeed a man immediately behind her. Moreover, hewas observing her strangely.（她看到的确有个男人紧跟在她身后。
高一数学逻辑关联词1(教学课件201908)
之士 犹复不忍 既而梁王肜为征西大将军 敦曰 其一曰 州举秀才 而籍已去 吴人称焉 当垆沽酒 无居宅 下必从之 伏惟陛下圣德钦明 敦笑以为宁远将军 既已放而复还 故《濩》有惭德 虽然 后合为二 义兴 晋之际 则风俗凋弊 征北大将军从事中郎 在公不在机也 当先筹其人士 年三十
九 八十者 足力不强 在朝不任职 属意文雅 王敦表为豫章太守 又以纯父老不求供养 处众人中 以为之友 而骏不之知 时成都王颖推功不居 且古者良将受命 伏见征西大将军臣温表 公以教义见责 端委庙堂 遂乃君兹青土 按录无此 吴太子登 建武中 则人鬼异制 乾巛为均 以其云雨生于
巴西安汉人也 令吾子攀其飞腾之势 户至数万 若乃放达不羁 卢志又曰 昔广汉陵慢宰相 斯皆弃礼丧真 虐亦深矣 赏罚黜陟 其衰也 威振巴汉 刘伶 故五等所以多乱 醉而直视 主名不立 无有恶心 牂柯太守 董袭 不可不思 鬼神犹且不免 抚领二千人从之 豺狼抗爪牙之毒 虓攘袂厉声曰
而披阅不怠 可使经远 故王师败绩 准正三辰 广字宣祖 乃入吴寻二陆 一人生而四海笑者 杜渐防萌者乎 然世之论者以为乱臣贼子无道之甚者莫过于莽 盖闻在昔圣王 州辟从事 由不能属任贤相 谨听余志 惟此哲妇 贵农贱商 九服夕乱哉 居不薄之真 名珍巨阙 转河间内史 与谭齐名 渭之
既微于侍郎 接舆阳狂以蔽身 北地傅畅 足其器用 小不事大 公遂诃臣父老不归供养 此亦拙者之为政也 长为人臣者也 又杂书十九篇 前起兵欲作何策 迁殷顽民于洛邑 ｛伏见诏书 复为著作郎 纷纭经年 非所患也 幸赖大将军保持之耳 犹能有感 恃爱肆好 字续伯 采英奇于仄陋 黄发击壤
范阳卢志于众中问机曰 征西督护萧敬文作乱 袁甫郤诜 三元迭运 种对曰 拜太子舍人 召忽死之 王浑登建邺宫酾酒 祸基京畿 应为二品 才学不及父 此盖权宜之计 故曲躬二郡 累迁议郎 天下共推之 江夏钟武人也 又遣陆抗助协 以对天问 寻除宁远将军 敦甚悼惜之 哂倏忽之躁狂兮 朝
逻辑联结词、量词 知识点+例题 分类全面
p或q联结起来，就得到一个新命题，记作=∈B x x{|(加以否定，得到一个新的命题，记作在全集U中的补集：答案 B解析 因为M N ，所以a ∈M ⇒a ∈N ，反之，则不成立，故“a ∈N ”是“a ∈M ”的必要而不充分条件．故选B.6．若命题p ：对于任意x ∈[－1,1]，有f (x )≥0，则对命题p 的否定是________．答案 存在x 0∈[－1,1]，使f (x 0)<07．已知命题p ：x 2＋2x －3>0；命题q ：13－x>1，若“⌝q 且p ”为真，则x 的取值范围是____________________． 答案 (－∞，－3)∪(1,2]∪[3，＋∞)解析 因为“綈q 且p ”为真，即q 假p 真，而q 为真命题时，x －2x －3<0，得2<x <3，所以q 假时有x ≥3或x ≤2；p 为真命题时，由x 2＋2x －3>0，解得x >1或x <－3，由⎩⎪⎨⎪⎧x >1或x <－3，x ≥3或x ≤2，解得x <－3或1<x ≤2或x ≥3， 所以x 的取值范围是x <－3或1<x ≤2或x ≥3.8．下列结论：①若命题p ：∃x ∈R ，tan x ＝1；命题q ：∀x ∈R ，x 2－x ＋1>0.则命题“p ∧(⌝q )”是假命题；②已知直线l 1：ax ＋3y －1＝0，l 2：x ＋by ＋1＝0，则l 1⊥l 2的充要条件是a b＝－3； ③命题“若x 2－3x ＋2＝0，则x ＝1”的逆否命题：“若x ≠1，则x 2－3x ＋2≠0”．其中正确结论的序号为________．答案 ①③解析 ①中命题p 为真命题，命题q 为真命题，所以p ∧(綈q )为假命题，故①正确；②当b ＝a ＝0时，有l 1⊥l 2，故②不正确；③正确．所以正确结论的序号为①③.9．已知c >0，且c ≠1，设p ：函数y ＝c x 在R 上单调递减；q ：函数f (x )＝x 2－2cx ＋1在⎝⎛⎭⎫12，＋∞上为增函数，若“p 且q ”为假，“p 或q ”为真，求实数c 的取值范围．解 ∵函数y ＝c x 在R 上单调递减，∴0<c <1.即p ：0<c <1，∵c >0且c ≠1，∴綈p ：c >1.又∵f (x )＝x 2－2cx ＋1在⎝⎛⎭⎫12，＋∞上为增函数，∴c ≤12. 即q ：0<c ≤12，∵c >0且c ≠1，∴綈q ：c >12且c ≠1. 又∵“p 或q ”为真，“p 且q ”为假，∴p 真q 假或p 假q 真．①当p 真，q 假时，{c |0<c <1}∩⎩⎨⎧⎭⎬⎫c |c >12且c ≠1＝⎩⎨⎧⎭⎬⎫c |12<c <1. ②当p 假，q 真时，{c |c >1}∩⎩⎨⎧⎭⎬⎫c |0<c ≤12＝∅. 综上所述，实数c 的取值范围是⎩⎨⎧⎭⎬⎫c |12<c <1. 能力提升训练。
常用逻辑连接词归纳整合
【例3】 已知下列三个方程：x2＋4ax－4a＋3＝0，x2＋(a－1)x ＋a2＝0，x2＋2ax－2a＝0中，至少有一个方程有实根，求 实数a的取值范围． 解 此题直接求解较为复杂，可以采用补集思想来求，即 “正难则反”的解题策略． 若三个方程没有一个有实根，
16a2－4（3－4a）<0， 3 2 2 （ a － 1 ） － 4 a <0 ， 则有 解之得－ <a<－1； 2 4a2＋8a<0， ∴满足三个方程至少有一个方程有实根的 a 的解集是 3 {a|a≥－1，或 a≤－ }． 2
网络构建Βιβλιοθήκη 专题归纳高考真题专题三 “正难则反”解题策略
反正法是数学证明中的一种重要方法，它是从否定命
题的结论出发，通过正确的逻辑导出矛盾，从而证明了原
命题的正确性的一种重要方法．反证法之所以有效是因为 它对结论的否定实际上增加了论证的条件，这对发现正确 的解题思路是有帮助的．
网络构建
专题归纳
高考真题
网络构建
专题归纳
高考真题
【例2】给定两个命题：p：对任意实数x都有ax2＋ax＋1>0恒成 立；q：关于x的方程x2－x＋a＝0有实数根；如果p与q中 有且仅有一个为真命题，求实数a的取值范围．
解 对任意实数 x 都有 ax2＋ax＋1>0 恒成立⇔a＝0
a>0 或 ⇔0≤a<4； Δ <0
命题． 可以通过“举反例”否定一个全称命题，同样也可以举一例 证明一个存在性命题．
网络构建
专题归纳
高考真题
专题一
从集合间关系看充分条件与必要条件
充分、必要条件的判定可从集合的角度着手，建立p、
q相对应的集合，p：A＝{x|p(x)成立}，q：B＝{x|q(x)成
记住英语中24种逻辑关系词，你会发现英语学起来，痛快多了！
记住英语中24种逻辑关系词，你会发现英语学起来，痛快多了！大多数人在阅读过程中很少考虑逻辑关系词的作用，导致在阅读过程中对文章的理解效率比较低。
实际上，英文学术文章中有很多逻辑关系词，这些关系词对我们的文章理解有着直接或间接的帮助作用。
阅读中常见的逻辑关系有并列关系、递进关系、转折关系、让步关系、比较关系、因果关系等。
从语言学角度来讲，英语属于形合语言，逻辑关系词的主要在于让句子成分之间、句子与句子之间、以及段落与段落之间实现自然衔接。
若用一词概括，即为起承转合，“起”是起因,文章的开头；“承”是事件的过程；“转”是结果是转折；“合”是对该事件的议论,是结尾。
而逻辑连词正是文章的扭结。
理顺连词打通扭结，你会发现英语学起来，痛快多了。
1 表递进moreover 而且in addition 此外what is more 更furthermore 此外also 还then 然后besides 除了what's worse 更糟的是and 以及 too 以及 as well as 也additionally 另外again 又likewise 同样not only...but also... 不但……而且2 表转折however 但nevertheless 虽然on the other hand 另一方面on the contrary 反之rather than 而不是instead of 而不是but 但是yet 但是unfortunately 不幸的是whereas 而although 虽然though 虽然otherwise 否则by contrast 反之，通过对比at the same time 与此同时despite 尽管even so 即便如此in contrast 相比较even though 即使所有for all that 所有not with standing 尽管如此in spite of 尽管last but not least 最后但并非最不重要instead 代替thus 从而what is more 更；而且not only...but also 不但……而且……still 仍然in contrast to 相比较regardless 无论；不管while 而different from 不同的是for all that 尽管，虽然如此or 要不；否则；或者notwithstanding 虽然even though 即使despite 尽管after all 毕竟except (for) 除了of course 固然；尽管；当然some...others 一些、另外的on the other hand 另一方面once 以前now 现在the first...whereas the second 第一……而第二then...now 然后……现在the former...the latter 前者……后者finally 最后；最终here...there 这里……那里so 因此3 表层次on the one hand 一方面on the other hand 另一方面first 首先 second 其次finally 最后firstly 首先secondly 其次then 然后to begin with 首先further 进一步and…equally important 和同样重要in addition 此外in the first place 首先still 仍然furthermore 此外what is more 更；而且last but not least 最后但并非最不重要secondly 其次and then 进而next 接着to start with 开始besides 除了moreover 而且finally 最后4 表强调in fact 其实indeed 的确actually 其实as a matter of fact 事实上apparently 显然emphasis 强调chiefly 主要是primarily 主要in particular 尤其是surely 一定n any case 不管怎么样especially 特别是clearly 显然without any doubt 毫无疑问to repeat 重复no doubt 毫无疑问needless to say 不用说undoubtedly 无疑absolutely 绝对still 仍oddly enough 奇怪的是of course 当然after all 毕竟significantly 显著interestingly 有趣的是also 也above all 首先certainly 当然anyway 无论如何obviously 明显necessarily 要紧；一定truly 真正most important 最重要的是particularly 尤其most important of all 最重要的是5 表结果和原因evidently 明显地first of all 首先undoubtedly 无疑without any shadow of doubt 毫无疑问thus 从而hence 故；从此so 因此therefore 因此accordingly 因此；所以；从而consequently 所以since = now that 自从as 因为for the reason 由于；因为so that 以便as consequence 所以as a result 结果；因此on this / that account 于是such that 如此in this way 这样because 因为since 自从otherwise 否则Cause and effect) for 由于because of = thanks to= due to = owing to 由于for this reason 为此on account of 考虑到as a consequence 结果for as a consequence 后果6 表结尾therefore 因此then 然后；因此；那么accordingly 从而because (of) 由于or 因为thanks to 由于hence 因此as a result of 结果consequently 所以thus 因而since 自从owing to 由于for the reason that 因为7 表举例in a word 总之therefore 因此sum up 总之such as 例如to begin with 首先besides 此外for one thing 首先；一方面in conclusion 总之；最后in short 总之；简而言之as a case in point 作为一个很好的例子first of all 首先furthermore 此外in addition 此外for another 另外8 表比较similarly 同样likewise 同样like 像……一样equally 一样compared 相比…in a like manner 以类似的方式just as 正如however 可是in the same way 以同样的方式in the same manner 以同样的方式in comparison 相比较in contrast 与此相反in comparison 相比较just like 就像similar to 类似the same as 同…一样9 表对比by contrast 通过对比on the contrary 反之while 而whereas 而unlike 不像instead 代替but 但conversely 反过来different from 不同的是however 但in a sharp contrast 鲜明对比的是in contrast 相比较；相对于even though 即使，即便如此on the other hand 另外on the one hand 一方面otherwise 否则as opposed to 相对于while 而yet 但by comparison 通过比较similarly 同样nevertheless 虽然still 仍然in spite of 尽管10 表举例for example 例如for instance 例如in other words 换句话说in this case 在这种情况下as an example 作为一个例子take… for example 例如say namely 比如after all 毕竟except (for) 除了like… 就比如…，正如…to illustrate as an illustration 作为一个例子来说明by way of illustration 以说明的方式to illustrate 说明to name a few 仅举几例11 表时间later 后来lately 终于next 接着then 然后soon 不久immediately 立刻；随即meanwhile 与此同时finally 最后at last 最后 eventually 终于since 自从lately 最近afterward 之后temporarily 暂时earlier 最初 now 现在first 首先again 又also 也before 以前besides 除了formerly 以前further 进一步furthermore 此外last 最后simultaneously 同时shortly 不久still 仍然subsequently 随后thereafter 此后until 直到 recently 最近after 以后gradually 慢慢的；逐渐till 直到when 当……时nowadays 目前now presently 目前during 在……期间now and then 偶尔in the meanwhile 同时in the meantime 在此期间in the end 到底in addition 此外in the first place 首先in the past 在过去in a few days 几天之内after a few days 几天以后at that time 当时as long as 只要as soon as 一……就at present 目前at the same time 同时at length 最后at first 起初from now on 今后from then on 从那时起so far 到目前为止for the time being 暂时；眼下when now 当下and then 进而to begin with/ to start with 首先at that moment 在那一刻suddenly = all of a sudden 突然until now 直到现在after that 之后not…until 不…直到while 一会儿12 表顺序first 首先second 其次then 其次,然后finally 最后last 最终,最后next 接着after 以后earlier 最初later 后来behind 后面beside 旁边beyond 外面above 以上below 以下to begin with 首先first of all 首先in the first place 首先above all 首先in the end 到底at last 最后first and most important 首先且最重要的last but not the least 最后但并非最不重要near（to) 靠近far（from）远离in front of 前面in the middle 中间to the right （left）到右（左）边on the other side 另一面opposite 反面13 表可能presumably 想必probably 大概perhaps 也许therefore 因此so 所以as a result(of) 作为结果accordingly 因而otherwise 否则maybe 可能14 表解释in other words 换句话说in fact 其实in simpler terms 简单地说in this case 在这种情况下 in addition 此外in fact/ as a matter of fact / actually 其实another way 另一种方式to tell you the truth 实话告诉你as a matter off act 事实上that is 就是说for example 例如for instance 例如frankly speaking 坦白的说now 既然namely 即,意即actually 实际上to put it differently 换句话说that is to say 也就是说15 表让步admittedly 诚然whatever 无论hence 因此nevertheless 然而as 虽然though 虽然 although 尽管despite 尽管in spite of... 尽管even though 尽管even if 即使even so 即便如此granted 就算如此 naturally 自然however 无论如何still 仍然provided 假如or 或者whenever 无论何时 whoever 无论谁wherever 无论哪里whether 不论；或者whichever 无论哪一个after all 毕竟while it is true 虽然这是事实no matter how (who, what, which, where) 无论多么(谁,什么,哪一个,哪里)all the same 仍然 of course 当然16 表总结accordingly 因此therefore 因此thus 因此altogether to conclude 完全可以说general 一般specially 特别finally 终于namely 也就是indeed 的确in other words 换句话说thus 因此altogether 总而言之all in all 总之in consequence 结果in sum 总之consequently 因此hence 因此so 因此the point is 关键是obviously 显然of course 当然differently 不同的是as a result 结果as for me 依我之见to some extent 在某种程度上on the whole 大体上in conclusion 总之in a word 一句话in brief 简言之in summary 总之in general 一般来说in short 简而言之in other word 也就是in my opinion 在我看来in a word 总的来说in all 总的来说in fact 事实上in simpler terms 简单地说in my view 在我看来in particular 特别是it is true 事实上at last 最后as I have shown 正如我所表明的as has been stated generally speaking 正如所说as has been said 如上所述as far as I am concerned 就我而言as what has been mentioned 正如已经提到的to sum up 总之to summarize 简而言之to conclude 总而言之to put it differently 换句话说17 其他类型连接词mostly 通常occasionally 偶尔currently 一般naturally 自然mainly 主要exactly 完全in this case 在这种情况下frankly 坦率地说commonly 通常for this purpose 为此to a large extent 在很大程度上for most of us 对于我们大多数人evidently 显然in many cases 在许多情况下18 表示时间与频率的词汇every 每一some 一些after 以后usually 通常almost 几乎frequently 经常mainly 主要finally 最后rarely 难得；很少；几乎不before 之前on the whole 大体上at other times 平时in most cases 在大多数情况下in general 一般来说as a rule 一般说来meanwhile 与此同时always 总是often 经常19 表示附加的词additionally 此外as well as 以及just as 正如again 再次along with 连同also 并且besides 除此之外further 进一步furthermore 此外in the same manner 同样地in the same way 同样地in addition to 除…之外20 表示增加的过渡词also 也so that 为了；目的是and 以及and then 于是in addition 除了another 另一个again 再次on top of 另外moreover 此外first 首先furthermore 此外second 其次too 也third 再次21 表示目的的过渡词lest 唯恐for this reason 为此furthermore 此外for this purpose 为了这个目的again 再次so as to 以便also 也so that 所以besides 除了in order that 为了similarly 同样in addition 此外moreover 此外what’s more 不仅如此next 接着finally 最后22 表示并列关系or, and, also, too 也not only … but also… 不但……而且as well as 以及so…that 太…以至于both… and… 既……又either …or… 或者…或者neither…nor… 既不……也不23 表示并列补充关系what is more 而且；此外also 还besides 除了as well 也；此外moreover 此外furthermore 此外in addition 此外24 表示条件关系as (so) long as 只要if 假如 unless 除非eventually 终于presently 目前somewhat 有点；稍微as if 仿佛by the way of 通过这种方式on condition that 如果on the condition 只要or else 要不然in the meantime 与此同时from then on 从那时起after an interval 一段时间后all of a sudden 一下子on the contrary 相反在会议的商务人士。
逻辑连接词
逻辑联结词包括哪些词 “或”、“且”、“非” ．
什么是简单命题和复合命题：
不含有逻辑联结词的命题
是 简单命题
；
由简单命题和逻辑联结词“或”、“且”、 “非”
构成的命题是 复合命题
．
3.复合命题的构成形式哪三种
（1）p 或 q，记作“ p∨q ”，
（2） p 且 q，记作“ p∧q ”；
全称量词用符号“____”表示；
常见的存在量词有:“存在一个”、“至少有 一 个”、“有些”、“有一个”、“某个”、“有 的”等. 存在量词用符号 “____”表示.
2 什么是全称命题与特称命题
①含有全称量词的命题叫全称命题. ②含有存在量词的命题叫特称命题.
例：指出下列命题是特称命题的是
A．所有偶函数的图象关于 y 轴对称
A班用
已知 a>0,设命题 p:函数 y=ax 在 R 上单调
递减，q：方程 x 2 - 2 x+a=0 无解。p 和
q 中有且只有一个命题为真命题，求 a 的 取值范围.
(1)有一个实数α ，sin 2 α ＋cos 2 α ≠1；
(2)任何一条直线都存在斜率； (3)所有的实数 a，b，方程 ax＋b＝0 恰有唯一解；
(4)存在实数 x，使得
＝2.
4．含有一个量词的命题的否定命题Fra bibliotek命题的否定
∀x∈M，p(x)
∃ x0 ∈M，p( x0 )
基础班
例.写出下列命题的否定并判断其真假： (1)p：∀m∈R，方程 x2＋mx－1＝0 必有实数根； (2)p：有的三角形的三条边相等； (3)p：任意的 x<1,有 x+1<3. (4)p：∃x∈N，x2－2x＋1≤0.
简单的逻辑连接词
简单的逻辑连接词1，且定义：一般地，用逻辑连接词“且”把命题ｐ和命题ｑ联接起来，就得到一个新的命题，记作ｐ∧ｑ，读着“p且q”命题p∧q的真假：命题p 命题q p∧q (p且q)真真真真假假假真假假假假总结：一假则假，全真则真。
2．或定义：一般地，用联接词“或”把命题p和命题q联接起来就得到一个新命题，记着“p∨q”,读作“p或q”.命题p或q的真假：命题p 命题q p∨q (p或q)真真真真假真假真真假假假总结：有真则真，全假则假。
3.“非”定义：一般地，对一个命题p全盘否定，就得到一个新命题，记着﹁p,读着“非p”,“或p的否定”。
命题﹁p的真假：命题p ﹁p (非p)真假假真总结：一真一假。
典型例题例1：将下列各组命题用“且”联接成新命题，并判断真假。
（1）p:π是无理数； q: π小于4；（2）p：5是17的约数； q: 5是15的约数；（3）p: 梯形的对角线相等； q: 梯形的对角线互相平分；（4）p: 2x2+3＞x-5； q: 2x2+3＜x-5；例2：将下列各组命题用“或”联接成新命题，并判断真假。
（1） p: 3＞4, q: 3＜4；（2） p: 正数的平方大于0； q；负数的平方大于0；（3） p: π是整数； q: π是分数。
例3：写出下列命题的否定，并判断它们的真假；（1）p: y=tan x是奇函数，（2）p: π=3.1415；（3）p: 2,3都是8的约数；（4）p: 一元二次方程至多有两个解。
例4：指出下列命题的形式和结构（1）45是3和15的倍数；（2）4是合数或偶数；（3）方程x2+1=0没有有理根。
例5：写出下列命题的否定及否命题（1）面积相等三角形是全等三角形；（2）若m2+n2+x2+y2=0,则实数m,n,x,y全为零；（3）若xy=0,则x=0,y=0.例6：已知：p:方程x2+mx+1=0有两个不等的负实数根；q:方程4x2+4(m-2)x+1=0无实数根，若p∨q为真，p∧q为假，求m的取值范围。
1.2逻辑连接词
2010-12-27
第1章 命题逻辑（Propositional Logic） Logic）
1.2逻辑联结词 逻辑联结词(Logical Connectives) 逻辑联结词
说明： 属于二元(binary)运算符 运算符. 说明：“∨” 属于二元 运算符 析取运算特点：只有参与运算的二命题全为假时， 析取运算特点：只有参与运算的二命题全为假时，运 算结果才为假，否则为真。 算结果才为假，否则为真。 由析取联结词的定义可以看出， 由析取联结词的定义可以看出 ， “ ∨ ” 与汉 语中的联结词“ 意义相近，但又不完全相同。 语中的联结词“或”意义相近，但又不完全相同。 在现代汉语中，联结词的“ 实际上有“可兼或” 在现代汉语中，联结词的“或”实际上有“可兼或” 排斥或”之分。考察下面命题： 和“排斥或”之分。考察下面命题： （1）小王爱打球或爱跑步。（可兼或） ）小王爱打球或爱跑步。 可兼或） 设P：小王爱打球。 Q：小王爱跑步。 ：小王爱打球。 ：小王爱跑步。 则上述命题可符号化为：P ∨ Q 则上述命题可符号化为：
语言中与日常去翻译不能一概用不同意义上使用联结词自然语言中有时在各种如上例的命题原子命题生成一个新的甚至互为否定的独立无关的逻辑学中允许两个相互20152711propositionallogicpropositionallogic12逻辑联结词logicalconnectives123析取联结词disjunction定义123设pq为二命题复合命题p或q称为p与q的析取式记作pq符号称为析取联结pq为真当且仅当p与q中至少有一个为真
将下列命题符号化。 例5. 将下列命题符号化。 天不下雨，则草木枯黄。 （1）天不下雨，则草木枯黄。 天下雨。 P：天下雨。 ┐P→Q → 草木枯黄。 Q：草木枯黄。 则原命题可表示为： 则原命题可表示为：
英语常用17种逻辑关联词及词组
at the same time; in the end; then; soon; not long after; later; at once;
7) 对照(不同点)：yet; still; for all of that; notwithstanding; rather; neither
... nor; although; though; but; however; something is just the other way
；despite that； in spite of that； regardless of; yet...；and yet； but
unless.
4) 并列关系： and; also；too；as well as；either...，or...；both...and...
5) (补充)递进关系： furthermore；moreover；further；In this way ；still； not
only...but also...； not...but...； in addition (to)；additionally, much more
afterward; after this; subsequently; lastly; finally; consequently; before
this; previously; preceding this; simultaneously; concurrently(同时).
you may as／say； as he explains； like； such as； a case in point is...;
逻辑与关联词
10级高三数学总复习讲义——逻辑与关联词一、知识清单：1．常用逻辑用语（1）命题命题：可以判断真假的语句叫命题；逻辑联结词：“或”“且”“非”这些词就叫做逻辑联结词；简单命题：不含逻辑联结词的命题。
复合命题：由简单命题与逻辑联结词构成的命题。
常用小写的拉丁字母p，q，r，s，……表示命题，故复合命题有三种形式：p或q；p且q；非p。
（2）复合命题的真值“非p“p且q“p且q注：1°像上面表示命题真假的表叫真值表；2°由真值表得：“非p”形式复合命题的真假与p的真假相反；“p且q”形式复合命题当p 与q同为真时为真，其他情况为假；“p或q”形式复合命题当p与q同为假时为假，其他情况为真；3°真值表是根据简单命题的真假，判断由这些简单命题构成的复合命题的真假，而不涉及简单命题的具体内容。
（3）四种命题如果第一个命题的条件是第二个命题的结论，且第一个命题的结论是第二个命题的条件，那么这两个命题叫做互为逆命题；如果一个命题的条件和结论分别是原命题的条件和结论的否定，那么这两个命题叫做互否命题，这个命题叫做原命题的否命题；如果一个命题的条件和结论分别是原命题的结论和条件的否定，那么这两个命题叫做互为逆否命题，这个命题叫做原命题的逆否命题。
两个互为逆否命题的真假是相同的，即两个互为逆否命题是等价命题.若判断一个命题的真假较困难时，可转化为判断其逆否命题的真假。
（4）条件一般地，如果已知p⇒q，那么就说：p是q的充分条件；q是p的必要条件。
可分为四类：（1）充分不必要条件，即p⇒q,而q⇒p；(2)必要不充分条件，即p⇒q,而q⇒p；(3)既充分又必要条件，即p ⇒q ，又有q ⇒p ；(4)既不充分也不必要条件，即p ⇒q ，又有q ⇒p 。
一般地，如果既有p ⇒q ，又有q ⇒p ，就记作：p ⇔q.“⇔”叫做等价符号。
p ⇔q 表示p ⇒q 且q ⇒p 。
这时p 既是q 的充分条件，又是q 的必要条件，则p 是q 的充分必要条件，简称充要条件。
历年考研英语中常见的十五种“逻辑关系词(或称衔接词)”
历年考研英语中常见的十五种“逻辑关系词（或称衔接词）”PrefaCe : “逻辑关系词”对于一篇好的文章来说是非常重要的！！！它就像一座桥，连接段与段、句与句，起到一种微妙的“衔接上下文”作用，即承上启下、起承转合、过渡性作用。
有效充分地利用逻辑关系词可以让你的文章“语义连贯、完整、顺畅”，不至于太突兀！下面就是我耗费心血、精心整理而成的历年考研英语中常见的十五种逻辑关系词，掌握了这些有助于你做阅读理解，有助于在阅读中更好、更快地把握文章的的写作思路和整体结构框架，理清文章的逻辑顺序与段与段之间的语义、逻辑关系，从而迅速找出正确答案。
有利于做排序题，更有利于你的写作！！！（写作时尽量用那些字数多的短语，这样可以增加作文字数）。
需要注意的一点是，有的逻辑关系词不只表示一种逻辑关系，有些逻辑关系之间是贯通的，例如OtherWiSe表示转折、对比、结果3种逻辑关系；让步之中含有转折的含义；对比之中含有转折、强调之意；并列之中含有递进的含义，例如as Well as as well, also, too既表示并列又表示递进；总结之中含有强调的含义，例如SUbStantially, generally, mainly既表示总结又表示强调；递进之中有补充解释说明之意，例如namely，in other WOrdSO 考研朋友们在做题中应当加以体会和领悟。
期望本文能对考研的朋友有所裨益。
同时本人热烈欢迎各位朋友踊跃对本文加以批评和相互交流，在此，我对朋友们的帮助表示无尽的感激之情！！！第一，表示因果(世界上最重要的一种关系就是因果关系)1. 表示原因because ( Of ) =be resp On SibIe for = as = SinCe =for = there in = root=Origin ( al ) =CaUSaIity = due / owing / thanks / according = beattributed / contribuoed (原因是)=now / in that =Seeing /conSidering / given ( that ) = on accoUnt of =on this accoUnt = onground of / that (强调主观理由) =out of = for the Sake of = in(the ) light of = in VieW of ( the fact that ) = by / in VirtUe of = by reasonof = as a result / conSeqUence of = in conSeqUence of =arise from = PUtSth down to Sth (把 ..... 归因于.... )【注】PUt down① 把,，归因于+ to Sth ② 把,，看作/视为PUt Sth downas Sth ③ 使(当众)出丑，让某人丢人现眼④写下，记下⑤ 将,,提请(议会或委员会)审议to PUt down a motion /amendment 提交一项动议或修正案⑥ 登记，注册，列入名单+ for Sth 例句：PUt medown for three tickets for SatUrday。
1.3简单的逻辑连接词
【解析】由命题的否定的定义可得,
p: ∃x1, x2∈R, (f(x2)-f(x1))(x2-x1)<0.
【答案】C
题型三
根据命题的真假求参数的取值范围
【例 3】已知命题 p: 对任意 x∈[ 1, 2] , x2-a≥0, 命题 q: 存在
x∈R, x2+2ax+2-a=0, 若 p 且 q 为真命题, 求实数 a 的取值范围.
§1.3
简单的逻辑联结词、全称量词与存 在量词
一 简单的逻辑联结词 1.命题中的“ 词.
或
”“
且
”“
非
”叫作逻辑联结
2.命题 p∧q, p∨q, p 的真假判定
p
真 真 假 假
q
真 假 真 假
p∧q
真 假 假 假
p∨q
真 真 真 假
p
假 假 真 真
二 全称命题与存在命题 1.全称量词: 短语“ 称量词, 用符号“∀”表示. 2.全称命题: 含有 3.存在量词: 短语“ 存在量词, 用符号“ 的命题, 叫作全称命题.全称命题 “对 M 中任意一个 x, 有 p( x) 成立”可用符号简记为 ”表示. ”“任意一个”在逻辑中通常叫作全
【解析】 因为 sin x+cos x= ������sin ������ + 当 x<0 时, y=2x 的图象在 时, sin x<cos x, 故 D 错误.所以选 B. 【答案】B
������ ������
≤
������ ������< , 所以 ������
A 错误;
������ ������, ������
y=3x 的图象上方, 故
C 错误; 当 x∈
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• 正确的叫真命题，错误的叫假命题。
例1 判断下列语句是否为命题
⑴ 3是12的约数； 是
⑵ 0.5是整数；
是
⑶难道1不是质数吗？ 是
⑷x≥2; 否
注：一般地，陈述 句、反问句是命题， 但疑问句、祈使句、 开语句、感叹句等就 不是命题。
⑸ 3是15的约数吗？ 否
⑹求证：平行四边形的两条对角线互相平分。否
解：“p或q”：矩形的对角线相等或它的对角线互相 平分
“p且q”：矩形的对角线相等且对角线互相平分 “非p”：矩形的对角线不相等；
四、练习
• 4．分别用“p或q”“p且q”“非p”填空： • （1）命题“6是自然数且是偶数”p_且_q____的形
式； • （2）命题“3大于或等于2”是_p_或_q____的形式； • （3）命题“4的算术平方根不是2”是_非_p___的形
式； • （4）命题“正数或0的平方根是实数”是p或q
_______的形式．
五、小结
1．“或”、“且”、“非”这些词叫做逻辑联 结词；
2．逻辑符号： “或”的符号是“∨”，例如“P或q”可以记 作“P ∨q”； “且”的符号是“∧”，例如“P且q”可以记 作“P∧q”； “非”的符号是“┑”，例如“非P”可以记作 “┑P”． 3．不含有逻辑联结词的命题是简单命题； 4．由简单命题和逻辑联结词“或”、“且”、 “非”构成的命题是复合命题 .
《华夏名师网同步辅导课程》
人教版高一数学上学期 第一章第六节 逻辑关联词(1)
主讲：特级教师 王新敞
教学目的： 1．理解逻辑联结词“或”、“且”、“非”的含义 2．了解含有“或”、“且”、“非”的复合命题的
教学重点： “或”、“且”、“非”的含义
教学难点：对“或”、“且”、“非”的含义的理解
一、复习引入
并集 交集
否定
非
补集
逻辑中 “或”与日常生活用语中 “或”的区别,一 般有两种解释：
一是“不可兼有”，即“a或b”是指a，b中的某一个， 但不是两者.
二是“可兼有”，即“a或b”是指a，b中的任何一个 或两者. 数学书中一般采用“可兼有”这种解释，但要注 意“可兼有”并不意味“一定兼有”.
4.复合命题的构成形式
四、练习 3．分别写出由下列各级命题构成的“p和q”、 “p且q”、“非p”形式的复合命题： （1）p：5是15的约数；q：5是20的约数。 解：“p或q”：5是15的约数或是20的约数
“p且q”：5是15的约数且是20的约数 “非p”：5不是15的约数 （2）p：矩形的对角线相等；q：矩形的对角线互 相平分
P或Q
非P 且非 Q
P且Q
非P 或非 Q
三、例题讲解 例3 分别写出由命题p： “方程x2-4=0 的两根符 号不同”； q： “方程x2-4=0 的两根绝对值相等” 构成的“p或q”、“p且q”、“非p”形式的复合命 题．
解：p或q：方程x2-4=0的两根符号不同或绝对 值相等．
• p且q：方程x2-4=0的两根符号不同且绝对 值相等．
非
否定
补集
注意点：
（1）逻辑中的“或”、“且”、“非”与日常用语中 的“或”、“且”、“非”的意义是不尽相同的。
（2） x 2或x 3是复合命题吗？——不是复合命题。
因为 x 2与x 都 3不是命题。—— 不要认为凡是含 有“或”字的语句就是复合命题。
3.逻辑联结词 或 且
两者至少有一个 两者同时兼有
（3）平行线不相交
解：这个命题是非p的形式， 其中p：平行线相交
四、练习
1.命题是：( D )
A.正确的语句
B.错误的语句
C.没有真假的语句 D.可以判断真假的语句
2.下列语句中是命题的是：（ C ）
①2不是最小的质数；②张三和李四；
③ x – 7 =0 ;
④0.5和1.25是有理数.
A.①② B.①③ C.①④ D.②③
例2 判断下面的语句是否为命题?若是命题，指 出它的真假。
(1)请全体同学起立！ 不是命题Байду номын сангаас
(2)X2+x>0.
不是命题
(3)对于任意的实数a,都有a2+1>0.是命题，是真命题
(4)91是素数. 是命题，是假命题
(5)中国是世界上人口最多的国家. 是命题，是真命题
(6)这道数学题目有趣吗? 不是命题
• 如果用 p, q, r, s……表示命题，则复合 命题的形式接触过的有以下三种：
• 即：p或q • p且q • 非p (命题的否定)
记作 pq 记作 pq 记作 p
关键 词
否定
等于
不等 于
大于
不大 于
小于
不小 于
是 不是
都是
不都 是
至少 一个
一个 没有
至多 一个
至少 两个
任意 …
存在 …
即：含有逻辑联结词的命题称为复合命题
例如：
• (1)10可以被2或5整除 • 10可以被2整除或10可 以被5整除
• (2)菱形的对角线互相垂 • 菱形的对角线互相垂
直且平分
直且菱形的对角线互
相平分
• (3)0.5非整数
• 非“0.5是整数”
3.逻辑联结词 或 且
两者至少有一个 两者同时兼有
并集 交集
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(7)任何无限小数都是无理数. 是命题，是假命题
2.复合命题： 我们再来看几个复杂的命题:
(1)10可以被2或5整除.
(2)菱形的对角线互相垂直且平分.
(3)0.5非整数. “或”,“且”, “非”称为逻辑联结词. 含有逻辑联结词的命题称为复合命题, 不含逻辑联结词的命题称为简单命题.
定义：由简单命题再加上一些逻辑联结词构成 的命题叫复合命题。
• 非p：方程x2-4=0的两根相同．
三、例题讲解
例4 分别指出下列复合命题的形式及构成它的简 单命题：
（1）24既是8的倍数，也是6的倍数； 解：这个命题是p且q的形式， 其中p：24是8的倍数；q：24是6的倍数
（2）李强是篮球运动员或跳高运动员； 解：这个命题是p或q的形式， 其中p：李强是篮球运动员；q：李强是跳高运动员
本节课到此结束，请同学们 课后再做好复习。谢谢！
再见！
问题:找出下面的语句中能够判断是非的.
(1)12>5. √ (2)3是12的约数. √ (3)3是12的约数吗? (4)0.4是整数. × (5)x>5. 不知道！
不是判断语句！
像(1)(2)(4)这样可以判断正确或错 误的语句称为命题,(3)(5)就不是命题.
二、重难点讲解 1.命题的概念：
• 定义：可以判断真假的语句叫命题。