電大離散數(shù)學(xué)期末考試試題(配答案)

1、廣東技術(shù)師范學(xué)院模擬試題 科 目：離散數(shù)學(xué) 考試形式：閉卷 考試時(shí)間: 120 分鐘系別、班級(jí)： 姓名： 學(xué)號(hào)： 一填空題（每小題2分，共10分）1. 謂詞公式的前束范式是_ xyp(x)q(y) _。2. 設(shè)全集則ab =_2_，_4,5_，_ 1,3,4,5 _3. 設(shè)，則_ c,a,c,b,c,a,b,c _，_。4. 在代數(shù)系統(tǒng)（n，+）中，其單位元是0，僅有 _1_ 有逆元。5如果連通平面圖g有個(gè)頂點(diǎn)，條邊，則g有_e+2-n_個(gè)面。二選擇題（每小題2分，共10分）1. 與命題公式等價(jià)的公式是（ ）（a） （b） （c） （d）2. 設(shè)集合,a上的二元關(guān)系不具備關(guān)系( )性質(zhì)（a）

2、(a)傳遞性 (b)反對(duì)稱性 (c)對(duì)稱性 (d)自反性3. 在圖中,結(jié)點(diǎn)總度數(shù)與邊數(shù)的關(guān)系是( )(a) (b) (c)(d) 4. 設(shè)d是有n個(gè)結(jié)點(diǎn)的有向完全圖,則圖d的邊數(shù)為( )(a) (b) (c) (d)5. 無向圖g是歐拉圖,當(dāng)且僅當(dāng)( )(a) g的所有結(jié)點(diǎn)的度數(shù)都是偶數(shù) (b)g的所有結(jié)點(diǎn)的度數(shù)都是奇數(shù)(c)g連通且所有結(jié)點(diǎn)的度數(shù)都是偶數(shù) (d) g連通且g的所有結(jié)點(diǎn)度數(shù)都是奇數(shù)。三計(jì)算題（共43分）1. 求命題公式的主合取范式與主析取范式。（6分）解：主合取方式：pqr(pqr)(pqr)(pqr)= 0.2.4主析取范式：pqr(pqr) (pqr) (pqr) (pqr

3、) (pqr)= .72. 設(shè)集合上的二元關(guān)系r的關(guān)系矩陣為,求的關(guān)系矩陣，并畫出r，的關(guān)系圖。（10分）3 無向圖g有12條邊，g中有6個(gè)3度結(jié)點(diǎn)，其余結(jié)點(diǎn)的度數(shù)均小于3，問g中至少有多少個(gè)結(jié)點(diǎn)？（10分）解：g（v,e），| e |=v，d（vi）3,設(shè)至少有x個(gè)節(jié)點(diǎn)，由握手定理得：212=d（vi）63+(x-6)328故g中至少有9個(gè)節(jié)點(diǎn)。4 求下面兩個(gè)圖的最小生成樹。（12分）5. 試判斷是否為格？說明理由。（5分）解：（z,）是格，理由如下：對(duì)于任意az，aa成立，滿足自反性；對(duì)于任意az，bz，若ab且ba，則a=b，滿足反對(duì)稱性；對(duì)于任意a，b，cz，若ab，bc

4、，則ac，滿足傳遞性；而對(duì)于任意a，bz，ab，b為最小上界，a為最大下界，故（z，）是格。（注：什么是格？）四證明題（共37分）1. 用推理規(guī)則證明。（10分）證明： 編號(hào)公式依據(jù)（1）（bc）c前提（2）bc，c（1）（3）b（2）（4）ab（3）（5）a（3）（4）（6）（ad）前提（7）ad（6）（8）d（5）（6）2. 設(shè)r是實(shí)數(shù)集，。求證：都是滿射，但不是單射。（10分）證明：要證f是滿射，即yr,都存在（x1，x2）rr，使f（x1，x2）=y，而f（x1，x2）=x1+x2，可取x1=0，x2=y，即證得；再證g是滿射，即yr，,都存在（x1，x2）rr，使g（x1，x2）=y

5、，而g（x1，x2）=x1x2，可取x1=1，x2=y，即證得；最后證f不是單射，f（x1，x2）=f（x2，x1）取x1x2，即證得，同理：g（x1，x2）=g（x2，x1），取x1x2，即證得。3. 無向圖g有9個(gè)結(jié)點(diǎn)，每個(gè)結(jié)點(diǎn)的度數(shù)不是5就是6，求證：g中至少有5個(gè)6度結(jié)點(diǎn)或6個(gè)5度結(jié)點(diǎn)。（10分）證明：設(shè)g中至多有4個(gè)6度結(jié)點(diǎn)且5個(gè)5度結(jié)點(diǎn)，d（vi）=49不是偶數(shù)，故它不是一個(gè)圖，矛盾。（下面只供參考，個(gè)人答案）4. 設(shè)平面上有100個(gè)點(diǎn)，期中任意兩點(diǎn)間的距離至少是1，則最多有300對(duì)點(diǎn)距離恰好為1。（7分）證明：設(shè)任意兩點(diǎn)間的讀書和恰好為1，則滿足：d（vi）=2ed（vi）661

6、002e e300故最多只有300條邊，即300對(duì)點(diǎn)距離恰好為1.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 international toure to discuss h

7、is 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 from somebody to pay them.it i

8、s 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 it is only with harsh sanctio

9、ns 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 league match at chelsea on sun

10、day.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 behaviour of their fans duringc

11、itys 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 racist insults from fans of cska.b

12、aumgartner 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 humidity and limited cloud cover. th

13、e 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 commercial airliners (5.6 mil

14、es/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 resembling an olympic diving plat

15、form.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 end.skydiver preps for the bi

16、g 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 spi

17、ns 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 au