2014年电大自考离散数学试题及答案.doc

全国自学考试离散物理习题课程代码：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唯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、多选或已选均无分。1．下列词语不是命题的是（D）A．中华人民共和国的首都是上海B．张三是学生C．雪是白色的D．太好了！2．下列方程不是谓词合式公式的是（B）A．（(x）P(x)→R(y)B．((x) ┐P（x）(((x)(P(x)→Q(x))C．((x)((y)(P(x)∧Q(y))→((x)R(x)D．((x)(P(x,y)→Q(x,z))∨((z)R(x,z)3．下列等式为重言式的是（）A．(┐P∧R)→QB．P∨Q∧R→┐RC．P∨(P∧Q)D．(┐P∨Q)((P→Q)4．在指定的解释下，下列公式为真的是（）A．((x)(P(x)∨Q(x)),P(x):x=1,Q(x):x=2,论域:{1,2}B．((x)(P(x)∧Q(x)),P(x):x=1,Q(x):x=2,论域: {1,2}C．((x)(P(x) →Q(x)),P(x):x>2,Q(x):x=0,论域:{3,4}D．((x)(P(x)→Q(x)),P(x):x>2,Q(x):x=0,论域:{3,4}5．对于公式((x) ((y)(P(x)∧Q(y))→((x)R(x,y)，下列表述正确的是（）A．y是自由变元B．y是约束变元C．((x)的辖域是R(x, y)D．((x)的辖域是((y)(P(x)∧Q(y))→((x)R(x,y)6．设论域为{1,2}，与公式((x)A(x)等价的是（）A．A(1)∨A(2)B．A(1)→A(2)C．A(1)∧A(2)D．A(2)→A(1)7．设Z+是正整数集，R是实数集，f:Z+→R, f(n)=log2n ,则f（）A．仅是入射B．仅是满射C．是双射D．不是函数8．下列关系矩阵所对应的关系具有反对称性的是（）A．B．C．D．9．设R1和R2是集合A上的相容关系，下列关于复合关系R1(R2的表述正确的是（）A．一定是等价关系B．一定是相容关系C．一定不是相容关系D．可能是也或许不是相容关系10．下列运算不满换律的是（）A．a*b=a+2bB．a*b=min(a,b)C．a*b=|a-b|D．a*b=2ab11．设A是偶数集合，下列表述正确的是（）A．<A,+>是群B．<A,×>是群C．<A,÷>是群D．<A,+>, <A,×>,<A,÷>都不是群12．设*是集合A上的二元运算，下列表述正确的是（）A．在A中有关于运算*的左幺元一定有右幺元B．在A中有关于运算*的左右幺元一定有幺元C．在A中有关于运算*的左右幺元，它们不必定相等D．在A中有关于运算*的幺元不必定有左右幺元13．题13图的最大出度是（）A．0B．1C．2D．314．下列图是欧拉图的是（）15．一棵树的3个4度点，4个2度点，其它的都是1度，那么这棵树的边数是（）A．13B．14C．15D．16二、填空题（本大题共10小题，每小题2分，共20分）请在每小题的括号中填上正确答案。

错填、不填均无分。16．请写出表示德摩根律的两个命题推导等价公式___________，17．n个命题变元的___________称为小项，其中每个变元与它的否定不能同时发生，但它们需要___________。18．前提引入规则：在证明的任何步骤上都可以___________，简称___________规则。19．自由变元代入规则是指对某___________出现的个体变元可用个体常元或用与原子公式中所有个体变元不同的个体变元去代入，且___________。20．设A=(,B={2,4}，则((A)=___________，A×B___________。21．设A={1,2,3,4}, A上的二元关系R={<1,2>,<2,4>,<3,3>},S={<1,3>,<2,4>,<4,2>}，则R2(S=___________，(R-1)2=___________。22．设代数系统<A,·,*>是环，则<A,·>是___________，<A,*>是___________。23．在<Z7-{0},(7>中，元素2的阶为___________，它生成的子群为___________，其中(7为模7乘法。

24．设<A,≤>是一个___________，如果A中任意两个元素都有___________，则称<A, ≤>为格。25．若一条___________中全国2014年7月自学考试离散数学试题和答案，所有的___________均不相似，称为迹。三、计算题（本大题共6小题，每小题5分，共30分）26．给定论域D={1,2}，f(1)=2, f(2)=1, S(1)=F, S(2)=T, G(1,2)=T, G(2,1)=T,在该数组下，求方程(x(S( f(x))∧G(x, f(x)))的真值。27．请通过等值演算法求┐(P∧Q)→(P∨Q)的主析取范式。28．设A={1,2,3,4}，给定A上二元关系R={<1,1>,<1,2>,<2,4>,<4,2>}，求R的释放闭包。29．对题29图图示格，找出它的所有的4元子格。30．用矩阵的方式求题30图中节点ui，u5之间宽度为2的模式的数量。31．求题31图的最小生成树。四、证明题（本大题共3小题，第32小题8分，第33、34小题各6分，共20分）32．用推理方式证明(A∨B)→(C∧D),(D∨F)→E├A→E。

33．证明：设<G,·>是一个群，则针对任意a,b∈G，必存在唯一的x∈G并且a·x=b。34．设图G有n个节点，n+1条边，证明：G中大约有一个结点度数≥3。五、应用题（本大题共2小题，第35小题9分，第36小题6分，共15分）35．符合化以下命题，并构造推理证明：三角函数都是周期函数，有些三角函数是连续函数全国2014年7月自学考试离散数学试题和答案，所以有些周期函数是连续函数。36．两个等价关系的并集不必定是等价关系，试举例说明。2010年7月全国自考离散物理习题参考答案"If we don't 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 FA's 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 Fifa's anti-racism taskforce, is in London for the Football Association's 150th anniversary celebrations and will attend City's 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 it's about how he felt and I would like to speak to him first to find out what his experience was."Uefa has?opened disciplinary proceedings against CSKA?for the "racist behaviour of their fans" during?City's 2-1 win.Michel Platini, president of European football's governing body, has also ordered an immediate investigation into the referee's actions.CSKA said they were "surprised and disappointed" by Toure's 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, he'll 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 it's 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 won't. 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 there好文档7全国2010年7月自学考试离散物理习题

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