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1、安徽大学 20 10 20 11 学年第2 学期 离散数学(下)考试试卷（A 卷）（闭卷时间120分钟）考场登记表序号一、单选题（每小题2分，共 20 分）1、设,G为群，其中G是实数集，运算为kbaba，k为G中固定常数，则在群,G中，关于运算的幺元以及元素x的逆元分别为（）Ae和x B-e和xk C k和kx2 D k和)2(kx2、设f是,G到,H的群同态，那么下列命题错误的是（）A同态f的核是,G的正规子群 B),(Gf的幺元必是,H的幺元C),(Gf的零元可以不是,H的零元 D 同态象),(Gf是,H的子群3、设21:RRf是环同态满射，baf)(，那么下列结论错误的是（）A若a是零
2、元，则b是零元 B若a是幺元，则b是幺元C若a不是零因子，则b不是零因子 D 若2R是不交换的，则1R不交换4设 R 为实数集合，20(),0aMRa bR Rb为实数域关于矩阵的乘法运算()A.可交换且有幺元B.可交换且无幺元C.不可交换且有幺元D.不可交换且无幺元5下面哈斯图为分配格的是（）A.B.C.D 6在布尔代数1,0,B中任取两元素ba,，下列命题与ab不一定等价的是（）题 号一二三四五六七总分得 分阅卷人院/系年级专业姓名学号答题勿超装订线-装-订-线-得 分A.*a ba B.abb C.*0a b D.1ab7布尔代数,*,0,1B上定义的n元布尔表达式所对应的不同主析取范式
3、总个数为（）A.2n B.|nBB C.2|nB D.|nB8设 G是连通平面图，G中有 6 个顶点 8 条边，则G的面的数目是（）A2 个 B4 个 C3 个 D5 个9下列各图不是哈密尔顿图的为()A.B,C.D 10完全二部图4,5K删去（）条边可以得到树。A 4 B10 C5 D12 二、判断题（对的打，错的打，每小题2 分，共 10 分）1在代数系统中，一个元素的逆元不一定是唯一。（）2若环R满足左消去律，那么R必定没有右零因子。（）3不满足分配率的格（非分配格）同样也满足模不等式。（）4无向简单图G的极小支配集必为G的极大独立集。（）5任何树（2 个顶点以上）的点连通度和边连通度都
4、是1。（）三、填空题（每小空2分，共 20 分）1.设Z是整数集，在Z上定义二元运算为bababa，其中和是数的加法和乘法，则代数系统,*Z的幺元是，零元是。2.设11,.,1,012N，12为模 12 加法，则群1212,N中元素 7 的阶为，元素4确定的子群9,6,3,0H的陪集为。3.布尔代数(,),a b c中，原子为，,a b的补元为。4.设图G的邻接矩阵为001011110M，则G的可达性矩阵为_ _。5.设e为无向完全图4K的一条边，则4eK的连通度为，匹配数为。得 分得 分文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4
5、J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R
6、6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D
7、2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2
8、S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L
9、8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q
10、9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4
11、G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N46.若一棵树有2 个结点度数为2，一个结点度数为3，3 个结点度数为4，其余是叶结点，则该树有 _ _个叶结点。四、解答题（每小题10分,共 30 分）1.给定集合654321,G，其中，3213211，3123212，1233213，2313214，1323215，2133216。G在合成运算下组成的群,G，试求,G的所有正规子群和每个正规子群的陪集。2.设布尔代数
12、1,0,1,0ba上的布尔表达式321321*,xxbxaxxxf，试求其主析取范式和主合取范式。得 分答题勿超装订线-装-订-线-文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5
13、ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文
14、档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4
15、G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W
16、5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N
17、4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4
18、J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N43.求图G（如下图所示）的支配数)(0G、点覆盖数)(0G、边覆盖数)(1G、独立数)(0G、匹配数)(1G、点连通度)(0G、边连
19、通度)(1G、点色数)(0G、边色数)(1G，结果填入下表。并给出图G的邻接矩阵A（结点与自身邻接，结点次序按字母顺序）。)(0G)(0G)(1G)(0G)(1G)(0G)(1G)(0G)(1G五、证明题（每小题10分，共 20 分）1.设3|,Fabi a bQ，其中i为虚数单元，和为常规的复数加法和乘法，试证明,*F是一个域。文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S
20、4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8
21、R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9
22、D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G
23、2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4
24、L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10
25、Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB
26、4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N42.证明若G是每个区域至少由k（3k）条边围成的连通平面图，其中n、m分别是图G的顶点数和边数，则(2)2k nmk。答题勿超装订线-装-订-线-文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5
27、ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文
28、档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4
29、G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W
30、5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N
31、4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4文档编码:CB4G2S4J4G8 HU7W4L8R6W5 ZG5W10Q9D2N4