电大全国4月自学考试离散数学试题(附答案)

专业好文档全国2009年4月自学考试离散数学试题（附答案）课程代码：02324一、单项选择题（本大题共15小题，每小题1分，共15分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。错选、多选或未选均无分。1下列为两个命题变元P，Q的小项是（）APQ PB PQC PQD PPQ2下列语句中是真命题的是（）A我正在说谎B严禁吸烟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设P：我们划船，Q：我们跑步。命题“我们不能既划船又跑步”符号化为（）A P QB P QC（PQ）D（ P Q）4命题公式（P（PQ）Q是（）A矛盾式B蕴含式C重言式D等价式5命题公式（PQ）R的成真指派是（）A000，001，110，B001，011，101，110，111C全体指派D无6在公式（）F（x，y）（ y）G（x，y）中变元x是（）A自由变元B约束变元C既是自由变元，又是约束变元D既不是自由变元，又不是约束变元7集合A=1，2，10上的关系R=|x+y=10，xA，yA，则R的性质是（）A自反的B对称的C传递的、对称的D反自反的、传递的8若R和S是集合A上的两个关系，则下述结论正确的是（）A若R和S是自反的，则RS是自反的B若R和S是对称的，则RS是对称的C若R和S是反对称的，则RS是反对称的D若R和S是传递的，则RS是传递的9R=，则下列不是t（R）中元素的是（）ABCD10设A=1，2，3，4，5，6，7，8，下列选项正确的是（）A1AB1，2，3AC4，5ADA11在自然数集N上，下列运算是可结合的是（）Aab=a-2bBab=mina，bCab=-a-bDab=|a-b|12在代数系统中，整环和域的关系是（）A整环一定是域B域不一定是整环C域一定是整环D域一定不是整环13下列所示的哈斯图所对应的偏序集中能构成格的是（）ABCD14设G为有n个结点的简单图，则有（）A(G)nB(G)nC(G)nD(G)n15具有4个结点的非同构的无向树的数目是（）A2B3C4D5二、填空题（本大题共10小题，每小题2分，共20分）请在每小题的空格中填上正确答案。错填、不填均无分。16（x）（y）（P（x，y）Q（y，z）xP（x，y）中x的辖域为_，x的辖域为_。17两个重言式的析取是_式，一个重言式与一个矛盾式的析取是_式。18设N是自然数集合，f和g是N到N的函数，且f（n）=2n+1，g（n）=n2，那么复合函数（ff）（n）=_（gf）（n）=_。19设复合函数gf是从A到C的函数，如果gf是满射，那么_必是满射，如果gf是入射，那么_必是入射。20设A=1，2，B=2，3，则A-A=_，A-B=_。21设S是非空有限集，代数系统中，其中P（S）为集合S的幂集，则P（S）对运算的单位元是_，零元是_。22在中，2的阶是_。23设是格，其中A=1，2，3，4，6，8，12，24，为整除关系，则3的补元是_。24在下图中，结点v2的度数是_。25设图D=，V=v1，v2，v3，v4，若D的邻接矩阵A=，则deg-（v1）=_，从v2到v4长度为2的路有_条。三、计算题（本大题共5小题，第26、27小题各5分，第28、29小题各6分，第30小题8分，共30分）26已知A=，1，B=，1，1，计算AB，AB，A的幂集P（A）。27构造命题公式（PQ）P）R的真值表。28下图给出了一个有向图。（1）求出它的邻接矩阵A；（2）求出A2，A3，A4及可达矩阵P。29求下列公式的主合取范式和主析取范式：P（ P（Q（ QR）30设A=1，2，3，4，6，8，12，24，R为A上的整除关系，试画的哈斯图，并求A中的最大元、最小元、极大元、极小元。四、证明题（本大题共3小题，第31、32小题各6分，第33小题8分，共20分）31在整数集Z上定义：，证明：是一个群。32R是集合A上自反和传递的关系，试证明：RR=R。33证明：边e是图G的一条割边，当且仅当图G中不存在包含边e的简单回路。五、应用题（本大题共2小题，第34小题6分，第35小题9分，共15分）34构造下面推理的证明。如果小张和小王去看电影，则小李也去看电影。小赵不去看电影或小张去看电影。小王去看电影。所以，当小赵去看电影时，小李也去。35今有n个人，已知他们中任何2人的朋友合起来一定包含其余n-2人。试证明：（1）当n3时，这n个人能排成一列，使得中间任何人是其两旁的人的朋友，而两头的人是其左边（或右边）的人的朋友。（2）当n4时，这n个人能排成一圆圈，使得每个人是其两旁的人的朋友。2009年4月自考全国离散数学参考答案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 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 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 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 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 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 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 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 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. 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 (5.6 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 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 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 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 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 there9全国2009年4月自学考试离散数学试题