電大離散數(shù)學(xué)期末考試試題(配答案)

1、專業(yè)好文檔廣東技術(shù)師范學(xué)院模擬試題 科 目：離散數(shù)學(xué) 考試形式：閉卷 考試時間: 120 分鐘系別、班級： 姓名： 學(xué)號： 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有個頂點，條邊，則g有_e+2-n_個面。二選擇題（每小題2分，共10分）1. 與命題公式等價的公式是（ ）（a） （b） （c） （d）2. 設(shè)集合,a上的二元關(guān)系不具備關(guān)系( )性

2、質(zhì)（a） (a)傳遞性 (b)反對稱性 (c)對稱性 (d)自反性3. 在圖中,結(jié)點總度數(shù)與邊數(shù)的關(guān)系是( )(a) (b) (c)(d) 4. 設(shè)d是有n個結(jié)點的有向完全圖,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)點的度數(shù)都是偶數(shù) (b)g的所有結(jié)點的度數(shù)都是奇數(shù)(c)g連通且所有結(jié)點的度數(shù)都是偶數(shù) (d) g連通且g的所有結(jié)點度數(shù)都是奇數(shù)。三計算題（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)

3、 (pqr) (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3度結(jié)點，其余結(jié)點的度數(shù)均小于3，問g中至少有多少個結(jié)點？（10分）解：g（v,e），| e |=v，d（vi）3,設(shè)至少有x個節(jié)點，由握手定理得：212=d（vi）63+(x-6)328故g中至少有9個節(jié)點。4 求下面兩個圖的最小生成樹。（12分）5. 試判斷是否為格？說明理由。（5分）解：（z,）是格，理由如下：對于任意az，aa成立，滿足自反性；對于任意az，bz，若ab且ba，則a=b，滿足反對稱性；對于任意a，b，cz，若

4、ab，bc，則ac，滿足傳遞性；而對于任意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，

5、x2）=y，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個結(jié)點，每個結(jié)點的度數(shù)不是5就是6，求證：g中至少有5個6度結(jié)點或6個5度結(jié)點。（10分）證明：設(shè)g中至多有4個6度結(jié)點且5個5度結(jié)點，d（vi）=49不是偶數(shù)，故它不是一個圖，矛盾。（下面只供參考，個人答案）4. 設(shè)平面上有100個點，期中任意兩點間的距離至少是1，則最多有300對點距離恰好為1。（7分）證明：設(shè)任意兩點間的讀書和恰好為1，則滿足：d（vi）=2ed（v

6、i）661002e e300故最多只有300條邊，即300對點距離恰好為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 disc

7、uss 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 from somebody to pay them

8、.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 it is only with harsh sa

9、nctions 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 o

10、n 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 behaviour of their fans du

11、ringcitys 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 c

12、ska.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 humidity and limited cloud cove

13、r. 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 commercial airliners (5.

14、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 resembling an olympic diving

15、 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 end.skydiver preps for t

16、he 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 o

17、r 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 automaticall