电大离散数学作业3答案(集合论部分).doc

形成性考核作业 专业好文档姓 名： 学 号： 得 分： 教师签名： 离散数学作业3离散数学集合论部分形成性考核书面作业本课程形成性考核书面作业共3次，内容主要分别是集合论部分、图论部分、数理逻辑部分的综合练习，基本上是按照考试的题型（除单项选择题外）安排练习题目，目的是通过综合性书面作业，使同学自己检验学习成果，找出掌握的薄弱知识点，重点复习，争取尽快掌握。本次形考书面作业是第一次作业，大家要认真及时地完成集合论部分的综合练习作业。要求：将此作业用a4纸打印出来，手工书写答题，字迹工整，解答题要有解答过程，要求2010年11月7日前完成并上交任课教师（不收电子稿）。并在03任务界面下方点击“保存”和“交卷”按钮，完成并上交任课教师。一、填空题 1设集合，则p(a)-p(b )= 1,2,2,3,1,3,1,2,3 ，a b= , 2设集合a有10个元素，那么a的幂集合p(a)的元素个数为 1024 3设集合a=0, 1, 2, 3，b=2, 3, 4, 5，r是a到b的二元关系，则r的有序对集合为 ,4设集合a=1, 2, 3, 4 ，b=6, 8, 12， a到b的二元关系r那么r1 , 5设集合a=a, b, c, d，a上的二元关系r=, , , ，则r具有的性质是反自反性6设集合a=a, b, c, d，a上的二元关系r=, , , ，若在r中再增加两个元素, ，则新得到的关系就具有对称性7如果r1和r2是a上的自反关系，则r1r2，r1r2，r1-r2中自反关系有 2 个8设a=1, 2上的二元关系为r=|xa，ya, x+y =10，则r的自反闭包为 , 9设r是集合a上的等价关系，且1 , 2 , 3是a中的元素，则r中至少包含 , 等元素10设集合a=1, 2，b=a, b，那么集合a到b的双射函数是 ,或, 二、判断说明题（判断下列各题，并说明理由）1若集合a = 1，2，3上的二元关系r=，则(1) r是自反的关系； (2) r是对称的关系 解：(1) 结论不成立 因为关系r要成为自反的，其中缺少元素 (2) 结论不成立 因为关系r中缺少元素 2如果r1和r2是a上的自反关系，判断结论：“r-11、r1r2、r1r2是自反的” 是否成立？并说明理由 解：结论成立 因为r1和r2是a上的自反关系，即iar1，iar2 由逆关系定义和iar1，得ia r1-1； 由iar1，iar2，得ia r1r2，ia r1r2所以，r1-1、r1r2、r1r2是自反的ooooabcd图一ooogefho3若偏序集的哈斯图如图一所示，则集合a的最大元为a，最小元不存在 错误，按照定义，图中不存在最大元和最小元。 4设集合a=1, 2, 3, 4，b=2, 4, 6, 8，判断下列关系f是否构成函数f：，并说明理由(1) f=, , , ； (2)f=, , ；(3) f=, , , (1) 不构成函数，因为它的定义域dom(f)a(2) 也不构成函数，因为它的定义域dom(f)a(3) 构成函数，首先它的定义域dom(f) =1, 2, 3, 4= a，其次对于a中的每一个元素a，在b中都有一个唯一的元素b，使f三、计算题1设，求：(1) (ab)c； (2) (ab)- (ba) (3) p(a)p(c)； (4) ab解：(1) (ab)c=11,3,5=1,3,5(2) (ab)- (ba)=1,2,4,5-1=2,4,5(3) p(a) =,1,4,1,4p(c)= ,2,4,2,4p(a)p(c)=1,1,4(4) ab= (ab)- (ba)= 2,4,52设a=1,2,1,2，b=1,2,1,2，试计算（1）（a-b）； （2）（ab）； （3）ab解：（1）（a-b）=1,2（2）（ab）=1,2(3) ab ,3设a=1，2，3，4，5，r=|xa，ya且x+y4，s=|xa，ya且x+y0，试求r，s，rs，sr，r-1，s-1，r(s)，s(r) 解： r=,s=rs=sr=r-1=,s-1=r(s)= ,s(r)= , 4设a=1, 2, 3, 4, 5, 6, 7, 8，r是a上的整除关系，b=2, 4, 6(1) 写出关系r的表示式； (2 )画出关系r的哈斯图； (3) 求出集合b的最大元、最小元 解：(1) r=,12346578关系r的哈斯图(2) (3) 集合b没有最大元，最小元是2四、证明题 1试证明集合等式：a (bc)=(ab) (ac)证：设，若xa (bc)，则xa或xbc，即 xa或xb 且 xa或xc即xab 且 xac ，即 xt=(ab) (ac)，所以a (bc) (ab) (ac) 反之，若x(ab) (ac)，则xab 且 xac， 即xa或xb 且 xa或xc，即xa或xbc，即xa (bc)，所以(ab) (ac) a (bc) 因此a (bc)=(ab) (ac)2试证明集合等式a (bc)=(ab) (ac)证明：设s=a(bc)，t=(ab)(ac)， 若xs，则xa且xbc，即 xa且xb 或 xa且xc， 也即xab 或 xac ，即 xt，所以st 反之，若xt，则xab 或 xac， 即xa且xb 或 xa且xc 也即xa且xbc，即xs，所以ts 因此t=s 3对任意三个集合a, b和c，试证明：若ab = ac，且a，则b = c 证明：设xa，yb，则ab， 因为ab = ac，故 ac，则有yc， 所以b c 设xa，zc，则 ac， 因为ab = ac，故ab，则有zb，所以cb 故得a=b 4试证明：若r与s是集合a上的自反关系，则rs也是集合a上的自反关系r1和r2是自反的，x a， r1， r2，则 r1r2， 所以r1r2是自反的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