电大离散数学期末考试试题(配答案)

专业好文档广东技术师范学院模拟试题 科 目：离散数学 考试形式：闭卷 考试时间: 120 分钟系别、班级： 姓名： 学号： 一填空题（每小题2分，共10分）1. 谓词公式的前束范式是_ xy¬P(x)Q(y) _。2. 设全集则AB =_2_，_4,5_，_ 1,3,4,5 _3. 设，则_ c,a,c,b,c,a,b,c _，_。4. 在代数系统（N，+）中，其单位元是0，仅有 _1_ 有逆元。5如果连通平面图G有个顶点，条边，则G有_e+2-n_个面。二选择题（每小题2分，共10分）1. 与命题公式等价的公式是（ ）（A） （B） （C） （D）2. 设集合,A上的二元关系不具备关系( )性质（A） (A)传递性 (B)反对称性 (C)对称性 (D)自反性3. 在图中,结点总度数与边数的关系是( )(A) (B) (C)(D) 4. 设D是有n个结点的有向完全图,则图D的边数为( )(A) (B) (C) (D)5. 无向图G是欧拉图,当且仅当( )(A) G的所有结点的度数都是偶数 (B)G的所有结点的度数都是奇数(C)G连通且所有结点的度数都是偶数 (D) G连通且G的所有结点度数都是奇数。三计算题（共43分）1. 求命题公式的主合取范式与主析取范式。（6分）解：主合取方式：pqr(pqr)(p¬qr)(¬pqr)= 0.2.4主析取范式：pqr(pqr) (pq¬r) (¬pqr) (¬p¬qr) (p¬qr)= 1.3.5.6.72. 设集合上的二元关系R的关系矩阵为,求的关系矩阵，并画出R，的关系图。（10分）3 无向图G有12条边，G中有6个3度结点，其余结点的度数均小于3，问G中至少有多少个结点？（10分）解：G（V,E），| E |=V，d（Vi）<3,设至少有x个节点，由握手定理得：2×12=d（Vi）<6×3+(x-6)×32<(x-6) = x>8故G中至少有9个节点。4 求下面两个图的最小生成树。（12分）5. 试判断是否为格？说明理由。（5分）解：（Z,）是格，理由如下：对于任意aZ，aa成立，满足自反性；对于任意aZ，bZ，若ab且ba，则a=b，满足反对称性；对于任意a，b，cZ，若ab，bc，则ac，满足传递性；而对于任意a，bZ，ab，b为最小上界，a为最大下界，故（Z，）是格。（注：什么是格？）四证明题（共37分）1. 用推理规则证明。（10分）证明： 编号公式依据（1）（¬BC）¬C前提（2）¬BC，¬C（1）（3）¬B（2）（4）AB（3）（5）¬A（3）（4）（6）¬（¬AD）前提（7）A¬D（6）（8）¬D（5）（6）2. 设R是实数集，。求证：都是满射，但不是单射。（10分）证明：要证f是满射，即yR,都存在（x1，x2）R×R，使f（x1，x2）=y，而f（x1，x2）=x1+x2，可取x1=0，x2=y，即证得；再证g是满射，即yR，,都存在（x1，x2）R×R，使g（x1，x2）=y，而g（x1，x2）=x1x2，可取x1=1，x2=y，即证得；最后证f不是单射，f（x1，x2）=f（x2，x1）取x1x2，即证得，同理：g（x1，x2）=g（x2，x1），取x1x2，即证得。3. 无向图G有9个结点，每个结点的度数不是5就是6，求证：G中至少有5个6度结点或6个5度结点。（10分）证明：设G中至多有4个6度结点且5个5度结点，d（Vi）=49不是偶数，故它不是一个图，矛盾。（下面只供参考，个人答案）4. 设平面上有100个点，期中任意两点间的距离至少是1，则最多有300对点距离恰好为1。（7分）证明：设任意两点间的读书和恰好为1，则满足：d（Vi）=2ed（Vi）66×1002e e300故最多只有300条边，即300对点距离恰好为1."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 fa