電大離散數(shù)學(xué)試題及答案(最佳版面)

1、專業(yè)好文檔全國(guó)自考離散數(shù)學(xué)試題課程代碼：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、多選或未選均無分。1.設(shè)p：天下大雨,q：他在室內(nèi)運(yùn)動(dòng),命題“除非天下大雨，否則他不在室內(nèi)運(yùn)動(dòng)”可符合化為（）a.pqb.pqc.pqd.pq2.下列命題聯(lián)結(jié)詞集合中，是最小聯(lián)結(jié)詞組的是（）a.， b.，c.，d.，3.下列命題為假命題的是（）a.如果2是偶數(shù)，那么一個(gè)公式的析取范式惟一b.如果2是偶數(shù)，那么一個(gè)公式的析取范式不惟一c.如果2是奇數(shù)，那么一個(gè)公式的析取范式惟一d.如果2是奇數(shù)，那么一個(gè)公

2、式的析取范式不惟一4.謂詞公式x(p(x)$yr(y)q(x)中變?cè)獂是（）a.自由變?cè)猙.約束變?cè)猚.既不是自由變?cè)膊皇羌s束變?cè)猟.既是自由變?cè)彩羌s束變?cè)?.若個(gè)體域?yàn)檎麛?shù)減，下列公式中值為真的是（）a.x$y(x+y=0)b.$yx(x+y=0)c.xy(x+y=0)d.$x$y(x+y=0)6.下列命題中不正確的是（）a.xx-xb.xx-xc.a=xx,則xa且xad.a-b=a=b7.設(shè)p=x|(x+1)24，q=x|x2+165x,則下列選項(xiàng)正確的是（）a.pqb.pqc.qpd.q=p8.下列表達(dá)式中不成立的是（）a.a(bc)=(ab) (ac)b.a(bc)=(ab) (

3、ac)c.(ab)c=(ac) (bc)d.(a-b) c=(ac)-(bc)9.半群、群及獨(dú)異點(diǎn)的關(guān)系是（）a.群獨(dú)異點(diǎn)半群b.獨(dú)異點(diǎn)半群群c.獨(dú)異點(diǎn)群半群d.半群群獨(dú)異點(diǎn)10.下列集合對(duì)所給的二元運(yùn)算封閉的是（）a.正整數(shù)集上的減法運(yùn)算b.在正實(shí)數(shù)的集r+上規(guī)定*為a*b=ab-a-b a,br+c.正整數(shù)集z+上的二元運(yùn)算*為x*y=min(x,y) x,yz+d.全體nn實(shí)可逆矩陣集合rnn上的矩陣加法11.設(shè)集合a=1，2，3，下列關(guān)系r中不是等價(jià)關(guān)系的是（）a.r=,b.r=,c.r=,d.r=,12.下列函數(shù)中為雙射的是（）a.f：zz,f(j)=j(mod)b.f：nn,f(j

4、)=c.f：zn,f(j)=|2j|+1d.f：rr,f(r)=2r-1513.設(shè)集合a=a,b, c上的關(guān)系如下，具有傳遞性的是（）a.r=,b.r=,c.r=,d.r=14.含有5個(gè)結(jié)點(diǎn)，3條邊的不同構(gòu)的簡(jiǎn)單圖有（）a.2個(gè)b.3個(gè)c.4個(gè)d.5個(gè)15.設(shè)d的結(jié)點(diǎn)數(shù)大于1，d=是強(qiáng)連通圖，當(dāng)且僅當(dāng)（）a.d中至少有一條通路b.d中至少有一條回路c.d中有通過每個(gè)結(jié)點(diǎn)至少一次的通路d.d中有通過每個(gè)結(jié)點(diǎn)至少一次的回路二、填空題(本大題共10小題，每小題2分，共20分)請(qǐng)?jiān)诿啃☆}的空格中填上正確答案。錯(cuò)填、不填均無分。16.設(shè)a=1,2,3，b=3,4,5，則aa=_，ab=_。17.設(shè)a=1

5、,2,3,4,5，raa，r=，,，則r的自反閉包r(r)=_。對(duì)稱閉包t(r)=_。18.設(shè)p、q為兩個(gè)命題，德摩根律可表示為_，吸收律可表示為_。19.對(duì)于公式x(p(x)q(x)，其中p(x)x=1,q(x)x=2,當(dāng)論域?yàn)?,2時(shí)，其真值為_ ,當(dāng)論域?yàn)?,1,2時(shí)，其真值為_。20.設(shè)frr,f(x)=x+3,grr,g(x)=2x+1,則復(fù)合函數(shù),。21.3個(gè)結(jié)點(diǎn)可構(gòu)成_個(gè)不同構(gòu)的簡(jiǎn)單無向圖，可構(gòu)成_個(gè)不同構(gòu)的簡(jiǎn)單有向圖。22.無向圖g=如左所示，則g的最大度(g)=_，g的最小度(g)=_。23.設(shè)圖g,v=v1,v2,v3,v4,若g的鄰接矩陣，則deg-(v1)=_ _,de

6、g+(v4)=_。24.格l是分配格，當(dāng)且僅當(dāng)l既不含有與_同構(gòu)的子格，也不含有與_同格的子格。25.給定集合a=1,2,3,4,5，在集合a上定義兩種關(guān)系：r=,s=,，則，。三、計(jì)算題（本大題共5小題，第26、27題各5分，第28、29題各6分，第30題8分，共30分）26.設(shè)a=a,b,c,d，a上的等價(jià)關(guān)系r=,ia，畫出r的關(guān)系圖，并求出a中各元素的等價(jià)類。27.構(gòu)造命題公式（pq） （pq）的真值表。28.求下列公式的主析取范式和主合取范式：p（qp）（pq）29.設(shè)a=a, b, c, d, e，r為a上的關(guān)系，r=，, , , ia，試畫的哈斯圖，并求a中的最大元，最小元，極大

7、元，極小元。30.給定圖g如圖所示，（1）g中長(zhǎng)度為4的路有幾條？其中有幾條回路？（2）寫出g的可達(dá)矩陣。四、證明題（本大題共3小題，第31、32題各6分，第33題8分，共20分）31.設(shè)（l，）是格，試證明：a, b, c l, 有a（bc）（ab）（ac）；a（bc）（ab）（ac）。32.設(shè)r是a上的自反和傳遞關(guān)系，如下定義a上的關(guān)系t，使得x, ya，tr(y, x)r。證明t是a上的等價(jià)關(guān)系。33.設(shè)有g(shù)=, v的結(jié)點(diǎn)數(shù)|v|=n，稱該圖為n階圖，若從結(jié)點(diǎn)vi到vj存在路，證明從vi到vj必存在長(zhǎng)度小于等于n-1的一條路。五、應(yīng)用題（本大題共2小題，第34題7分，第35題8分，共15

8、分）34.構(gòu)造下面推理的證明。 每個(gè)喜歡步行的人都不喜歡坐汽車，每個(gè)人或者喜歡坐汽車或者喜歡騎自行車。有的人不喜歡騎自行車，因而有的人不喜歡步行。35.今要將6人分成3組（每組2個(gè)人）去完成3項(xiàng)任務(wù)。已知每個(gè)人至少與其余5個(gè)人中的3個(gè)人能相互合作。 （1）能否使得每組的2個(gè)人都能相互合作？ （2）你能給出幾種不同的分組方案？2008年4月全國(guó)自考離散數(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 a

9、fter fifa vice-president jeffrey webb - also in london 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 bee

10、n decided by the fifa congress that it is a nonsense 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.w

11、e can do something better to fight racism and discrimination.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-rac

12、ism taskforce, is in london for the football associations 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 spea

13、k to him first to find out what his experience was.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

14、 said they were surprised and disappointed by toures 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 mi

15、ssion. starting at the ground, conditions have to 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 cli

16、mb higher than the tip of mount everest (5.5 miles/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 wi

17、ll slowly drift to the edge of space at 120,000 feet ( 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 desp

18、ite 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 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 completely.if he goes too fast or spins out of control, he has a stabilizatio