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1、專業(yè)好文檔離散數(shù)學（本）復習題1設A=1，2，B=2，3，4，求r(AB)，r(A)r(B)。 2設A=a，b，c，問IA，EA是否具有自反性，反自反性，對稱性，反對稱性，傳遞性？3R，S是集合A上的兩個關系。試證明下列等式：（1）(RS)-1= S-1R-1（2）(R-1)-1= R（3）(RS)-1= R-1S-1（4）(RS)-1= R-1S-14設R是集合A上的關系，令R+=(x, y)|xA，yA，并且存在n0，使得xRny，則稱R+是R的傳遞閉包，證明：R+是包含R的最小具有傳遞性的關系。5若非空集合上的非空關系R是反自反的，是對稱的，試證明R不是傳遞的。6A=1，2，3，4，5，

2、6，7，8，9，10，R為A上的整除關系，請給出A的Hasse圖，并求出所有的極大元素，極小元素，最大元素，最小元素。7設G是含有3個不同原子的命題公式，當G是恒假公式的時候，G的主析取范式中有多少極小項，主合取范式中有多少極大項？8有人說：“等價關系中的反身性可以不要，因為反身性可以從對稱性和傳遞性推出：由對稱性，從a b可得b a，再由傳遞性得a a”。你的意見呢？9若集合A上的關系R，S具有對稱性，證明：RS具有對稱性的充要條件為RS= SR。 10若R是等價關系，試證明R-1也是等價關系。11給P和Q指派真值1，給R和S指派真值0，求出下面命題的真值：a) (P(QR)(PQ)(RS)

3、b) (PQ)R)(PQ)R)S)c) (PQ)R)(QP)(RS)d) (P(Q(RP)(QS)12指出下列公式哪些是恒真的哪些是恒假的：(1)P（P Q）Q(2)（P Q）（PQ）(3)（P Q） （QR）（P R ）(4)（P Q）（P QP Q）13設S=G1，Gn是命題公式集合。試求出在不增加新原子的情況下從S出發(fā)演繹出的所有命題公式。14證明下面的等價式：(1) (P(QR)(QR)(PR)=R(2) P(QP)=P(PQ)(3) P(QR)=(PQ)(PR)(4) (PQ)(RQ)=(PR)Q15找出下面公式的Skolem范式：(1)(xP(x)$yzQ(y，z)； (2)x(E

4、(x，0)($y(E(y，g(x)z(E(z，g(x)E(y，z)。16G=(P，L)是有限圖，設P(G)，L(G)的元數(shù)分別為m，n。證明：n ，其中 表示m中取2的組合數(shù)。17設G是有限圖，M，A分別是G的關聯(lián)矩陣和相鄰矩陣，證明：MM和A2的對角線上的元素是G中所有點的度。18設G為圖（可能無限），無回路，但若任意外加一邊于G后就形成一回路，試證G必為樹。19試舉出一個連通的(即漠視為圖后是連通的)，但無根的有向圖。20設G是有向圖，其中含一有向路(e1，en)，其中fin(en)=init(e1)，證明：G不是有向樹。21設(I，+)為整數(shù)加群，（5I，+）為I的子群，請給出mI的所有

5、陪集。22證明：若一個圖G的任意兩點度數(shù)之和n-1，n=|P(G)|，則該圖有Hamilton路。23給出一個具有5個點的邊數(shù)最多的非Hamilton圖。24給出代數(shù)格的定義。25設G為有向圖，若G具有有向樹定義中的1)和2)，并且沒有有向回路。問：若G有限，G是否是有向樹？若G不是有限的，如何？26設 * 是集合S上的二元代數(shù)運算，且滿足結(jié)合律，設x，y是S中任意元素，如果x * y = y * x，則x = y。試證明 * 滿足等冪律。27請給出一個布爾代數(shù)。28設R,S是A上的傳遞關系，證明或者反駁：(1) RS是傳遞關系；(2) RS是傳遞關系。29試用演繹法證明PQ，QR，PM，M共

6、同蘊涵R(PQ)30. 求證G的任意多個子群的交集是G的子群。并且，G的任意多個正規(guī)子群的交集仍是G的正規(guī)子群。31設H是G的子群。N是G的正規(guī)子群。命HN為H的元素乘N的元素所得的所有元素的集合。求證HN是G的子群。32設H是群G的一個有限非空子集，求證只要H中任意兩個元素的積仍在H內(nèi)，則H是G的子群。33求證循環(huán)群的子群仍是循環(huán)群。34求證若G的元數(shù)是一個質(zhì)數(shù)，則G必是循環(huán)群。35設K和H都是群G的子群，試證明：若HK是G的子群，則KH = HK。36什么是等價關系？37如果A上的一個等價關系為R，如何求出一個等價類？38給出命題公式PQ的真值表。39Skolem范式中的母式有什么特點？4

7、0有根的有向圖，是否一定是強連通的？41最優(yōu)樹是否一定唯一？42什么是體？43什么是代數(shù)格？44半序子格與代數(shù)子格是什么關系？If we dont do that it will go on and go on. We have to stop it; we need the courage to do it.His comments came hours after Fifa vice-president Jeffrey Webb - also in London for the FAs celebrations - said he wanted to meet Ivory Coast in

8、ternational Toure to discuss his complaint.CSKA general director Roman Babaev says the matter has been exaggerated by the Ivorian and the British media.Blatter, 77, said: It has been decided by the Fifa congress that it is a nonsense for racism to be dealt with with fines. You can always find money

9、from somebody to pay them.It is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. It is all nonsense.We can do something better to fight racism and discrimination.This is one of the villains we have today in our game. But

10、 it is only with harsh sanctions that racism and discrimination can be washed out of football.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier

11、League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist b

12、ehaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no raci

13、st insults from fans of CSKA.Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidi

14、ty and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of

15、 commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something res

16、embling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow

17、 end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him complet

18、ely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy t

19、his chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there4