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0004 离散数学
1.[单选题]整数集合Z关于数的加法“+”和数的乘法“×”构成的代数结构(Z, +, ×)是( )
奥鹏作业答案可以联系QQ 761296021
A.有零因子环
B.域和整环
C.整环
D.域
2.[单选题]设p：我们划船，q：我们跑步, 则有命题“我们不能既划船又跑步”符号化为( )
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463486483099467.png" title="201608291472463486483099467.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463496691067223.png" title="201608291472463496691067223.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463472252076958.png" title="201608291472463472252076958.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463510500026860.png" title="201608291472463510500026860.png" alt="blob.png"/>
3.[单选题]设集合A中有4个元素，则A上的等价关系共有( )个
A.14
B.16
C.15
D.13
4.[单选题]设R í A ′ A，S í A ′ A，则下述结论正确的是( )
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462307991044238.png" title="201608291472462307991044238.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462319270022308.png" title="201608291472462319270022308.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462328036019244.png" title="201608291472462328036019244.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462336998037005.png" title="201608291472462336998037005.png" alt="blob.png"/>
5.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461683092044742.png" title="201608291472461683092044742.png" alt="blob.png"/>
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461731468063560.png" title="201608291472461731468063560.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461763256081655.png" title="201608291472461763256081655.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461751665038482.png" title="201608291472461751665038482.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461740744054269.png" title="201608291472461740744054269.png" alt="blob.png"/>
6.[单选题]设集合A中有4个元素，则A上的划分共有( )个
A.15
B.14
C.13
D.16
7.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460659608056015.png" title="201608291472460659608056015.png" alt="blob.png"/>
A.B.幂等律
B.交换律
C.结合律
D.消去律
8.[单选题]设集合A中有99个元素，则A的子集有( )个
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461456245092362.png" title="201608291472461456245092362.png" alt="blob.png"/>
B.100
C.99
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461470498092835.png" title="201608291472461470498092835.png" alt="blob.png"/>
9.[单选题]域与整环的关系为( )
A.A. 域是整环
B.D.域不是整环
C.整环不是域
D.整环是域
10.[单选题]不同构的(5, 3)简单图有( )个
A.2
B.3
C.4
D.5
11.[单选题]下列偏序集，( )是格
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460902297061420.png" title="201608291472460902297061420.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460881135064094.png" title="201608291472460881135064094.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460893025074066.png" title="201608291472460893025074066.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460871862004688.png" title="201608291472460871862004688.png" alt="blob.png"/>
12.[单选题]下列联结词中，不满足交换律的是( )
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461632550033559.png" title="201608291472461632550033559.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461623240005742.png" title="201608291472461623240005742.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461644354046970.png" title="201608291472461644354046970.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461658030042117.png" title="201608291472461658030042117.png" alt="blob.png"/>
13.[单选题]设A, B, C是集合，则下述论断正确的是( )
A.C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462242394070974.png" title="201608291472462242394070974.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462233426028059.png" title="201608291472462233426028059.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462223378091131.png" title="201608291472462223378091131.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462204923046299.png" title="201608291472462204923046299.png" alt="blob.png"/>
14.[单选题]集合A = {1, 2, 3, 4}上的关系 R= {(1, 4), (2, 3), (3, 1), (4, 3)}, 则下列不是t(R)中元素的是( )
A.(1, 1)
B.(1, 2)
C.(1, 3) 微信7612 96021
D.(1, 4)
15.[单选题]具有4个结点的非同构的无向树的数目是( )
A.2
B.3
C.4
D.5
16.[单选题]设集合A中有4个元素，则A上的划分共有( )个.
A.13
B.14
C.15
D.16
17.[单选题]<img title="1460374140461024812.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374140461024812.png"/>
A.<img title="1460374181655048768.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374181655048768.png"/>
B.<img title="1460374210997021639.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374210997021639.png"/>
C.<img title="1460374237809074307.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374237809074307.png"/>
D.<img title="1460374265630069312.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374265630069312.png"/>
18.[单选题]<img title="1460203630269025115.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160409/1460203630269025115.png"/>
A.偏序关系
B.等价关系
C.相容关系
D.以上答案都不对
19.[单选题]<img title="1460366279162057512.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460366279162057512.png"/>
A.偏序
B.等价
C.相容
D.线性序
20.[单选题]设集合A中有99个元素，则A的子集有( )个.
A.<img title="1460361527937040692.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361527937040692.png"/>
B.99
C.<img title="1460361570276880171.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361570276880171.png"/>
D.100
21.[单选题]设集合A中有4个元素，则A上的等价关系共有( )个.
A.13
B.14
C.15
D.16
22.[单选题]集合A = {1, 2, …, 10}上的关系R ={(x, y)|x + y = 10, x, y ∈A}, 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
23.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460752232008078.png" title="201608291472460752232008078.png" alt="blob.png"/>
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460805988082806.png" title="201608291472460805988082806.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460821514047196.png" title="201608291472460821514047196.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460791899067229.png" title="201608291472460791899067229.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460837925091993.png" title="201608291472460837925091993.png" alt="blob.png"/>
24.[单选题]设集合A = {1, 2, 3, 4, 5}上的关系R = {(x, y)|x, y ? A且x + y = 6}，则R的性质是( )
A.对称的、传递的
B.反自反的、传递的
C.自反的
D.对称的
25.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457865087089992.png" title="201608291472457865087089992.png" alt="blob.png"/>
<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457882427070385.png" title="201608291472457882427070385.png" alt="blob.png"/>
A.F.传递
B.等价
C.对称
D.自反
26.[单选题]在谓词逻辑中，下列各式中不正确的是( )
A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462394047046361.png" title="201608291472462394047046361.png" alt="blob.png"/>
B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462385423040158.png" title="201608291472462385423040158.png" alt="blob.png"/>
C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462404417085118.png" title="201608291472462404417085118.png" alt="blob.png"/>
D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462376673085814.png" title="201608291472462376673085814.png" alt="blob.png"/>
27.[单选题]
<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457810380047161.png" title="201608291472457810380047161.png" alt="blob.png"/>
A.0
B.x
C.y
D.1
28.[判断题]任意整数都是0的因数.
A.正确
B.错误
29.[主观填空题]设|X| = n, P(X)为集合X的幂集, 则| P(X)| = ________. 在代数结构(P(X), ∪)中，则P(X) 对∪运算的单位元是________, 零元是________
A.
30.[主观填空题]不同构的5阶无向树有( )棵，不同构的5阶根树有( )棵
A.
31.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457711547063329.png" title="201608291472457711547063329.png" alt="blob.png"/>
A.
32.[主观填空题]在同构意义下，3阶群有( )个，4阶群有( )个，5阶群有( )个
A.
33.[主观填空题]设集合A = {1, 2, 3}，则A上的置换共有( )个
A.
34.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463281667027112.png" title="201608291472463281667027112.png" alt="blob.png"/>
A.
35.[主观填空题]集合A上的等价关系R必满足( 、 、 )
A.
36.[主观填空题]若G有8条边，3度和5度顶点各1个，其余都是2度项点，则G中有______个节点.
A.
37.[主观填空题]所有6的因数组成的集合为( ).
A.
38.[主观填空题]对于任意集合A, 若|A| = n, 则A的幂集合P(A)有( )个元素.
A.
39.[主观填空题]设A = {1, 2, 3, 4}，A上的二元关系R = {(1，2)，(2，3)，(3，2)}，S = {(l，3)，(2，3)，(4，3)}，则 (R - S)-1 = {___________}.
A.
40.[主观填空题]有限域的元素个数为( ), 其中( )且( )
A.
41.[主观填空题]<img title="1460365492340000296.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460365492340000296.png"/>
A.
42.[主观填空题]( )无向图称为无向树.
A.
43.[主观填空题]三个元素集合的划分共有( )种.
A.
44.[主观填空题]设<em>A </em>= {<em>a</em>, <em>b</em>}, <em>B </em>= {2, 4}，则<em>A </em>× <em>B </em>= {____<u> </u>_______}.
A.
45.[主观填空题]<img title="1460386196250034746.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460386196250034746.png"/>
A.
46.[主观填空题]<img title="1460199719009029273.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160409/1460199719009029273.png"/>
A.
47.[主观填空题]集合A上的等价关系R必满足( 、 、 ).
A.
48.[主观填空题]<img title="1459516404192080270.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160401/1459516404192080270.png"/>
A.
49.[主观填空题]设集合A = {1, 2, 3}，则A上的置换共有( )个.
A.
50.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463234629093235.png" title="201608291472463234629093235.png" alt="blob.png"/>
A.
51.[主观填空题]设G是(7, 15)简单平面图，则G一定 ( )连通图，其每个面恰由( )条边围成，G的面数为( )
A.
52.[主观填空题]任意6阶群的平凡子群一定是( )群
A.
53.[问答题]若n个人，每个人恰有3个朋友，则n必为偶数，试证明之
A.
54.[问答题]已知A ={{?}, {?, 1}}, B = {{?, 1}, {1}}, 计算A∪B, A+B，A的幂集P(A)
A.
55.[问答题]设G是一棵无向树且有2个4度节点，3个3度节点，其余均为叶节点.(1)求出该无向树共有多少个节点.
(2)画出两棵不同构的满足上述要求的无向树.
A.
56.[问答题]非零实数集合R*关于乘法运算“×”所构成的代数结构(R*, ×)与实数集合R关于加法运算+所构成的代数结构(R, +)同构吗，为什么?
A.
57.[问答题]画出所有不同构的5阶无向树.
A.
58.[问答题]画出所有不同构的4阶根树.
A.
59.[问答题]设<em>R</em>是集合<em>A</em>上自反和传递的关系，试证明：<em>R</em><img width="11" height="11" src="http://zuoye.eduwest.com/ueditor/themes/default/images/spacer.gif"/><em>R</em>=<em>R</em>
A.
60.[问答题]设G是(6，12) 的简单连通平面图，则G的面由多少条边围成，为什么？
A.
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