電大全國(guó)4月自學(xué)考試離散數(shù)學(xué)試題(附答案)

1、專業(yè)好文檔全國(guó)2009年4月自學(xué)考試離散數(shù)學(xué)試題（附答案）課程代碼：02324一、單項(xiàng)選擇題（本大題共15小題，每小題1分，共15分）在每小題列出的四個(gè)備選項(xiàng)中只有一個(gè)是符合題目要求的，請(qǐng)將其代碼填寫在題后的括號(hào)內(nèi)。錯(cuò)選、多選或未選均無(wú)分。1下列為兩個(gè)命題變?cè)猵，q的小項(xiàng)是（）apq pb pqc pqd ppq2下列語(yǔ)句中是真命題的是（）a我正在說(shuō)謊b嚴(yán)禁吸煙c如果1+2=3，那么雪是黑的d如果1+2=5，那么雪是黑的3設(shè)p：我們劃船，q：我們跑步。命題“我們不能既劃船又跑步”符號(hào)化為（）a p qb p qc（pq）d（ p q）4命題公式（p（pq）q是（）a矛盾式b蘊(yùn)含式c重言式d等價(jià)

2、式5命題公式（pq）r的成真指派是（）a000，001，110，b001，011，101，110，111c全體指派d無(wú)6在公式（）f（x，y）（ y）g（x，y）中變?cè)獂是（）a自由變?cè)猙約束變?cè)猚既是自由變?cè)?，又是約束變?cè)猟既不是自由變?cè)?，又不是約束變?cè)?集合a=1，2，10上的關(guān)系r=|x+y=10，xa，ya，則r的性質(zhì)是（）a自反的b對(duì)稱的c傳遞的、對(duì)稱的d反自反的、傳遞的8若r和s是集合a上的兩個(gè)關(guān)系，則下述結(jié)論正確的是（）a若r和s是自反的，則rs是自反的b若r和s是對(duì)稱的，則rs是對(duì)稱的c若r和s是反對(duì)稱的，則rs是反對(duì)稱的d若r和s是傳遞的，則rs是傳遞的9r=，則下列不是t（

3、r）中元素的是（）abcd10設(shè)a=1，2，3，4，5，6，7，8，下列選項(xiàng)正確的是（）a1ab1，2，3ac4，5ada11在自然數(shù)集n上，下列運(yùn)算是可結(jié)合的是（）aab=a-2bbab=mina，bcab=-a-bdab=|a-b|12在代數(shù)系統(tǒng)中，整環(huán)和域的關(guān)系是（）a整環(huán)一定是域b域不一定是整環(huán)c域一定是整環(huán)d域一定不是整環(huán)13下列所示的哈斯圖所對(duì)應(yīng)的偏序集中能構(gòu)成格的是（）abcd14設(shè)g為有n個(gè)結(jié)點(diǎn)的簡(jiǎn)單圖，則有（）a(g)nb(g)nc(g)nd(g)n15具有4個(gè)結(jié)點(diǎn)的非同構(gòu)的無(wú)向樹(shù)的數(shù)目是（）a2b3c4d5二、填空題（本大題共10小題，每小題2分，共20分）請(qǐng)?jiān)诿啃☆}的空格

4、中填上正確答案。錯(cuò)填、不填均無(wú)分。16（x）（y）（p（x，y）q（y，z）xp（x，y）中x的轄域?yàn)開(kāi)，x的轄域?yàn)開(kāi)。17兩個(gè)重言式的析取是_式，一個(gè)重言式與一個(gè)矛盾式的析取是_式。18設(shè)n是自然數(shù)集合，f和g是n到n的函數(shù)，且f（n）=2n+1，g（n）=n2，那么復(fù)合函數(shù)（ff）（n）=_（gf）（n）=_。19設(shè)復(fù)合函數(shù)gf是從a到c的函數(shù)，如果gf是滿射，那么_必是滿射，如果gf是入射，那么_必是入射。20設(shè)a=1，2，b=2，3，則a-a=_，a-b=_。21設(shè)s是非空有限集，代數(shù)系統(tǒng)中，其中p（s）為集合s的冪集，則p（s）對(duì)運(yùn)算的單位元是_，零元是_。22在中，2的階是_。23

5、設(shè)是格，其中a=1，2，3，4，6，8，12，24，為整除關(guān)系，則3的補(bǔ)元是_。24在下圖中，結(jié)點(diǎn)v2的度數(shù)是_。25設(shè)圖d=，v=v1，v2，v3，v4，若d的鄰接矩陣a=，則deg-（v1）=_，從v2到v4長(zhǎng)度為2的路有_條。三、計(jì)算題（本大題共5小題，第26、27小題各5分，第28、29小題各6分，第30小題8分，共30分）26已知a=，1，b=，1，1，計(jì)算ab，ab，a的冪集p（a）。27構(gòu)造命題公式（pq）p）r的真值表。28下圖給出了一個(gè)有向圖。（1）求出它的鄰接矩陣a；（2）求出a2，a3，a4及可達(dá)矩陣p。29求下列公式的主合取范式和主析取范式：p（ p（q（ qr）30設(shè)

6、a=1，2，3，4，6，8，12，24，r為a上的整除關(guān)系，試畫的哈斯圖，并求a中的最大元、最小元、極大元、極小元。四、證明題（本大題共3小題，第31、32小題各6分，第33小題8分，共20分）31在整數(shù)集z上定義：，證明：是一個(gè)群。32r是集合a上自反和傳遞的關(guān)系，試證明：rr=r。33證明：邊e是圖g的一條割邊，當(dāng)且僅當(dāng)圖g中不存在包含邊e的簡(jiǎn)單回路。五、應(yīng)用題（本大題共2小題，第34小題6分，第35小題9分，共15分）34構(gòu)造下面推理的證明。如果小張和小王去看電影，則小李也去看電影。小趙不去看電影或小張去看電影。小王去看電影。所以，當(dāng)小趙去看電影時(shí)，小李也去。35今有n個(gè)人，已知他們中任

7、何2人的朋友合起來(lái)一定包含其余n-2人。試證明：（1）當(dāng)n3時(shí)，這n個(gè)人能排成一列，使得中間任何人是其兩旁的人的朋友，而兩頭的人是其左邊（或右邊）的人的朋友。（2）當(dāng)n4時(shí)，這n個(gè)人能排成一圓圈，使得每個(gè)人是其兩旁的人的朋友。2009年4月自考全國(guó)離散數(shù)學(xué)參考答案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 lo

8、ndon for the fas celebrations - said he wanted to meet ivory coast international 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 nonsen

9、se for racism to be dealt with with fines. you can always find money 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 disc

10、rimination.this is one of the villains we have today in our game. but 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 assoc

11、iations 150th anniversary celebrations and will attend citys premier 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

12、.uefa hasopened disciplinary proceedings against cskafor the racist behaviour 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 tour

13、es complaint. in a statement the russian side added: we found no racist 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

14、be very calm - winds less than 2 mph, with no precipitation or humidity 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

15、/8.85 kilometers), drifting even higher than the cruising altitude of 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 fe

16、et ( then, i would assume, he will slowly step out onto something resembling 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

17、the deep end of a pool. it will be like he is diving into the shallow 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

18、 air closer to earth. but this will not be enough to stop him completely.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 this chute successfully, he will have to slow to 172 mph (277 kph). he will have a reserve parachute that will open a