《离散数学X》20春东大在线平时作业
20春学期《离散数学X》在线平时作业31.[单选题] <
2.[单选题]
正确答案:——A——
3.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12252476675311.bmp"></img>
A.矛盾式
B.重言式
C.无法确定
D.不知道
正确答案:——B——
4.[单选题] 下面是"xC(x),$x(A(x)ÚB(x)), "x(B(x)®ØC(x))Þ $xA(x)的谓词推理过程。在这个过程中每一步中的()处是此步所用的推理规则。请写出这些推理规则。⑴ $x(A(x)ÚB(x)), ( )⑵ A(a)ÚB(a) ( )⑴⑶ "xC(x) ( ) ⑷ C(a) ( )⑶⑸ "x(B(x)→ØC(x)) ( ) ⑹ B(a)→ØC(a) ( )⑸⑺ ØB(a) ( )⑷ ⑹ I12⑻ A(a) ( )⑵ ⑺ I10⑼ $xA(x)) ( ) ⑻
A.⑴ P;⑵ T; ⑶ T;⑷ UG;⑸ P;⑹ US;⑺ P;⑻ T;⑼ ES。
B. ⑴ P;⑵ EG;⑶ T;⑷ UG;⑸ P;⑹ UG;⑺ P;⑻ T;⑼ EG。
C. ⑴ P;⑵ ES;⑶P;⑷ US;⑸ P;⑹ US;⑺ T;⑻ T;⑼ EG。
D.⑴ P;⑵ US;⑶ T;⑷ UG;⑸ P;⑹ UG;⑺ P;⑻ T;⑼ UG。
正确答案:————
5.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12252465743431.bmp"></img>
A.重言式
B.矛盾式
C.无法确定
D.不知道
正确答案:————
6.[单选题] X,Y 是有限集合,|X|=m,|Y|=n。可以构成 ( )个从X到Y的函数。
A.mn
B. mn
C.2mn
D.nm
正确答案:————
7.[单选题] 令命题P表示“没有大学生不懂外语。”下面命题( )与P等价。
A.有些大学生懂一些外语。
B. 所有大学生都懂一些外语。
C. 有些大学生懂所有外语。
D. 没有大学生懂所有外语。
正确答案:————
8.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12253274357031.bmp"></img>
A.等价
B.不等价
C.无法确定
D.不知道
正确答案:————
9.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12253261108121.bmp"></img>
A.B:①:⑵⑶⑺⑻
B.B:②:⑶⑷⑻
C.B:③:⑶⑹⑺⑻
D.B:④:⑶⑺
正确答案:————
10.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12263081901091.bmp"></img>
A.f是满射,g是入射。
B.f是双射,g是双射
C.f是入射,g是满射。
D.f是入射,g是入射。
正确答案:————
11.[多选题] <p>试题见图片<img height="384" width="512" alt="" src="http://file.open.com.cn/ItemDB/43594/fd1f5147-a9e5-4105-8480-90f647d697fa/2009101020251752.JPG" /></p>
A.a图
B.b图
C.c图
D.d图
E.e图
F.f图
G.g图
H.h图
I.i图
J.j图
正确答案:————
12.[多选题] 下面的命题公式中哪些是永真式,只写出题号即可<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062290326512.bmp"></img>
A.1
B.2
C.3
D.4
正确答案:————
13.[多选题] 多选填空题。给定集合A={1,2,3},定义A上的等价关系如下:S={<1,1>,<1,2>,<2,1>,<2,2>,<3,3>}等价关系S中含有等价类( )。
A.{1}
B.{2}
C.{3}
D.{1,2}
E.{1,3}
F. {2,3}
G. {1,2,3}
正确答案:————
14.[多选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062356992111.bmp"></img>
A.A:⑴⑵⑶
B.B:⑴⑵⑷
C.C:⑵⑶⑷
D.D:⑴⑵⑶⑷
正确答案:————
15.[多选题] <p>试题见图片<img height="384" width="512" alt="" src="http://file.open.com.cn/ItemDB/43594/aa0897be-b269-47c2-8596-f7af09723b49/20091010204014761.JPG" /></p>
A.A图
B.B图
C.C图
正确答案:————
16.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069049348413.bmp" />
A.错误
B.正确
正确答案:————
17.[判断题] R是A上关系,判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069173734311.bmp" />
A.错误
B.正确
正确答案:————
18.[判断题] 判断题 。判断下面的说法是否正确。R和S都是A上任何传递关系,则R∩S 也传递。
A.错误
B.正确
正确答案:————
19.[判断题] 设A={a,{a},{a,b},{{a,b},c}},判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068844868714.bmp" />
A.错误
B.正确
正确答案:————
20.[判断题] 设A={a,{a},{a,b},{{a,b},c}},判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068830159312.bmp" />
A.错误
B.正确
正确答案:————
21.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069060918714.bmp" />
A.错误
B.正确
正确答案:————
22.[判断题] 判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068787532812.bmp" />
A.错误
B.正确
正确答案:————
23.[判断题] R和S都是A上关系,判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069155251514.bmp" />
A.错误
B.正确
正确答案:————
24.[判断题] R和S都是A上关系,判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069147623413.bmp" />
A.错误
B.正确
正确答案:————
25.[判断题] 判断题,判断下面说法是否正确。“对于整数集合I上的减法运算“-”来说, 0是幺元。”
A.错误
B.正确
正确答案:————
20春学期《离散数学X》在线平时作业1
1.[单选题] 单选填空题:设G是有向简单图,其结点度数序列为(2,2,3,3),入度序列为(0,0,2,3)。则结点的出度序列为( )。
A. (2,2,3,3)
B. (1,1,0,0)
C.(2,2,1,0)
D. (2,2,0,0)
正确答案:——C——
2.[单选题] 选择填空题。如果A、B都是有限集,且|A|=m, |B|=n,则 |A´B |=( ) 。
A.m+n ;
B. mn ;
C.mn ;
D. nm 。
正确答案:——B——
3.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12253274357031.bmp"></img>
A.等价
B.不等价
C.无法确定
D.不知道
正确答案:——A——
4.[单选题] <img src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257793747341.bmp"></img>
A.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794101562.bmp"></img>
B.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794423593.bmp"></img>
C.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794637964.bmp"></img>
D.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794850315.bmp"></img>
正确答案:————
5.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12263081901091.bmp"></img>
A.f是满射,g是入射。
B.f是双射,g是双射
C.f是入射,g是满射。
D.f是入射,g是入射。
正确答案:————
6.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257656827651.bmp"></img>
A.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657027962.bmp"></img>
B.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657182653.bmp"></img>
C.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657315624.bmp"></img>
D.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657514535.bmp"></img>
正确答案:————
7.[单选题] 命题公式(P®Q)®Q的主合取范式是( )。
A.P∨ØQ;
B.P∨Q;
C.(ØP∨Q)∧(P∨ØQ );
D.(P∨Q )∧(Ø P∨ØQ ) 。
正确答案:————
8.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257665293281.bmp"></img>
A.自然数集合
B.整数集合
C.有理数集合
D.实数集合
正确答案:————
9.[单选题] 设.X、Y 是有限集合,|X|=3,|Y|=2,可以构成( )个是从X到Y的入射函数。
A. 0
B.1
C. 2
D.3
正确答案:————
10.[单选题] 单选题。结点是树的内结点,当且仅当 该结点( )。
A.度数是大于2;
B.度数大于1;
C.度数不为0。
正确答案:————
11.[多选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062356992111.bmp"></img>
A.A:⑴⑵⑶
B.B:⑴⑵⑷
C.C:⑵⑶⑷
D.D:⑴⑵⑶⑷
正确答案:————
12.[多选题] <p>试题见图片<img height="384" width="512" alt="" src="http://file.open.com.cn/ItemDB/43594/fd1f5147-a9e5-4105-8480-90f647d697fa/2009101020251752.JPG" /></p>
A.a图
B.b图
C.c图
D.d图
E.e图
F.f图
G.g图
H.h图
I.i图
J.j图
正确答案:————
13.[多选题]多选题。 令I是整数集合;N是自然数集合,R是实数集合。+是加法运算,×是乘法运算。下面所列代数系统哪些是独异点?
A.<I,+>,
B. <R,+>,
C.<I,×>,
D. <N,×>,
E.<R,×>。
正确答案:————
14.[多选题]多选填空题。给定集合A={1,2,3},定义A上的等价关系如下:T=A×A(完全关系(全域关系))等价关系T中含有等价类( )。
A.{1}
B.{2}
C.{3}
D.{1,2}
E.{1,3}
F. {2,3}
G. {1,2,3}
正确答案:————
15.[多选题] 下面的命题公式中哪些是永真式,只写出题号即可<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062290326512.bmp"></img>
A.1
B.2
C.3
D.4
正确答案:————
16.[判断题] 判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068762328112.bmp" />
A.错误
B.正确
正确答案:————
17.[判断题] 设A={a,{a},{a,b},{{a,b},c}},判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068844868714.bmp" />
A.错误
B.正确
正确答案:————
18.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069049348413.bmp" />
A.错误
B.正确
正确答案:————
19.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069023946811.bmp" />
A.错误
B.正确
正确答案:————
20.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069042104612.bmp" />
A.错误
B.正确
正确答案:————
21.[判断题] 设A={Φ},B=P(P(A))。判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069066164015.bmp" />
A.错误
B.正确
正确答案:————
22.[判断题] 判断题 。判断下面的说法是否正确。R和S都是A上任何传递关系,则R∩S 也传递。
A.错误
B.正确
正确答案:————
23.[判断题] 判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068934371811.bmp" />
A.错误
B.正确
正确答案:————
24.[判断题] R和S都是A上关系,判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069147623413.bmp" />
A.错误
B.正确
正确答案:————
25.[判断题] 判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068951743713.bmp" />
A.错误
B.正确
正确答案:————
20春学期《离散数学X》在线平时作业2
1.[单选题]单选填空题。E是全集,E={a,b},E的幂集P(E)上的交运算Ç的有逆元的元素是( )。
A.Φ;
B. {a} ;
C.{b};
D. {a,b};
E.不存在。
正确答案:——D——
2.[单选题] <img src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257793747341.bmp"></img>
A.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794101562.bmp"></img>
B.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794423593.bmp"></img>
C.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794637964.bmp"></img>
D.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257794850315.bmp"></img>
正确答案:——C——
3.[单选题] 下面是"xC(x),$x(A(x)ÚB(x)), "x(B(x)®ØC(x))Þ $xA(x)的谓词推理过程。在这个过程中每一步中的()处是此步所用的推理规则。请写出这些推理规则。⑴ $x(A(x)ÚB(x)), ( )⑵ A(a)ÚB(a) ( )⑴⑶ "xC(x) ( ) ⑷ C(a) ( )⑶⑸ "x(B(x)→ØC(x)) ( ) ⑹ B(a)→ØC(a) ( )⑸⑺ ØB(a) ( )⑷ ⑹ I12⑻ A(a) ( )⑵ ⑺ I10⑼ $xA(x)) ( ) ⑻
A.⑴ P;⑵ T; ⑶ T;⑷ UG;⑸ P;⑹ US;⑺ P;⑻ T;⑼ ES。
B. ⑴ P;⑵ EG;⑶ T;⑷ UG;⑸ P;⑹ UG;⑺ P;⑻ T;⑼ EG。
C. ⑴ P;⑵ ES;⑶P;⑷ US;⑸ P;⑹ US;⑺ T;⑻ T;⑼ EG。
D.⑴ P;⑵ US;⑶ T;⑷ UG;⑸ P;⑹ UG;⑺ P;⑻ T;⑼ UG。
正确答案:——C——
4.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257656827651.bmp"></img>
A.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657027962.bmp"></img>
B.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657182653.bmp"></img>
C.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657315624.bmp"></img>
D.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257657514535.bmp"></img>
正确答案:————
5.[单选题] 单选填空题:对于自然数集合N上的加法运算“+”,13=( )。
A. 0;
B.1;
C.3;
D.6。
正确答案:————1647861640
6.[单选题]设命题P、Q所代表的意义如下:P:天气好。Q:我去旅游。命题“只有天气好,我才去旅游。”的符号表达式为:( )
A.P®Q,
B.Q® P,
C.Ø P ® Q,
D.Ø Q ® P
正确答案:————
7.[单选题] 选择填空题。R是A上关系,如果R是自反的,当且仅当 ( )。
A.A中有些元素x,有<x,x>∈R ;
B.所有A中元素x,都有<x,x>∈R ;
C.所有A中元素x,y,如果有<x,y>∈R ,也有< y, x >∈R;则x=y 。
正确答案:————
8.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12263081901091.bmp"></img>
A.f是满射,g是入射。
B.f是双射,g是双射
C.f是入射,g是满射。
D.f是入射,g是入射。
正确答案:————
9.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662070001.bmp"></img>
A.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662257182.bmp"></img>
B.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257662635783.bmp"></img>
C.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257663253904.bmp"></img>
D.<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257663473905.bmp"></img>
正确答案:————
10.[单选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/12257665293281.bmp"></img>
A.自然数集合
B.整数集合
C.有理数集合
D.实数集合
正确答案:————
11.[多选题] 下面的命题公式中哪些是永真式,只写出题号即可<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062290326512.bmp"></img>
A.1
B.2
C.3
D.4
正确答案:————
12.[多选题] <p>试题见图片</p><p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA; mso-bidi-font-size: 12.0pt"><v:group id="_x0000_s1026" style="MARGIN-TOP: 57.15pt; Z-INDEX: 1; LEFT: 0px; MARGIN-LEFT: 118.5pt; WIDTH: 333pt; POSITION: absolute; HEIGHT: 132.85pt; TEXT-ALIGN: left" coordsize="6660,2657" coordorigin="2340,4135"><font size="3"><font face="宋体, MS Song"> <v:shapetype id="_x0000_t202" coordsize="21600,21600" path="m,l,21600r21600,l21600,xe" o:spt="202"><v:stroke joinstyle="miter"></v:stroke><v:path o:connecttype="rect" gradientshapeok="t"></v:path></v:shapetype></font></font><v:shape id="_x0000_s1027" style="LEFT: 2520px; WIDTH: 600px; POSITION: absolute; TOP: 5028px; HEIGHT: 425px" stroked="f" fillcolor="#0c9" filled="f" type="#_x0000_t202"><v:textbox style="mso-next-textbox: #_x0000_s1027"><table cellspacing="0" cellpadding="0" width="100%"><tbody><tr><td style="BORDER-RIGHT: #ece9d8; 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flip: x" to="8820,6900" from="8460,6588"></v:line></v:group><v:line id="_x0000_s1087" style="POSITION: absolute" to="6120,6228" from="5400,6228"></v:line></v:group><img height="384" width="512" alt="" src="http://file.open.com.cn/ItemDB/43594/0709db06-5cc5-4899-a7fc-9135015ecb48/20091010201544845.JPG" /></span></p>
A.a 图
B.b图
C.c图
D.d图
E.e图
F.f图
G.g图
H.h图
I.i图
J.j图
正确答案:————q164 7861640
13.[多选题] 多选题。令P(E)是全集E的幂集;Ç是集合的交运算;È是集合的并运算;Å是集合的对称差运算。下面所列代数系统哪些是半群?
A.<P(E),Ç >,
B.< P(E), È>,
C.<P(E), Å>。
正确答案:————
14.[多选题] <img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123062356992111.bmp"></img>
A.A:⑴⑵⑶
B.B:⑴⑵⑷
C.C:⑵⑶⑷
D.D:⑴⑵⑶⑷
正确答案:————
15.[多选题]多选题。令P(E)是全集E的幂集;Ç是集合的交运算;È是集合的并运算;Å是集合的对称差运算。下面所列代数系统哪些是独异点?
A.<P(E),Ç >,
B.< P(E), È>,
C. <P(E), Å>。
正确答案:————
16.[判断题] R是A上关系,判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069185339013.bmp" />
A.错误
B.正确
正确答案:————
17.[判断题] R和S都是A上关系,判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069141981212.bmp" />
A.错误
B.正确
正确答案:————
18.[判断题] R是A上关系,判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069173734311.bmp" />
A.错误
B.正确
正确答案:————
19.[判断题] 设A={a,{a},{a,b},{{a,b},c}},判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068840920313.bmp" />
A.错误
B.正确
正确答案:————
20.[判断题] 判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068778675011.bmp" />
A.错误
B.正确
正确答案:————
21.[判断题] R和S都是A上关系,判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123069136082811.bmp" />
A.错误
B.正确
正确答案:————
22.[判断题] 判断下面命题的正误“不是所有完全图Kn都是欧拉图,但是所有完全图Kn都是汉密尔顿图。”
A.错误
B.正确
正确答案:————
23.[判断题] 设A={a,{a},{a,b},{{a,b},c}},判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068820410911.bmp" />
A.错误
B.正确
正确答案:————
24.[判断题] 判断下面命题的真值。<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068960454614.bmp" />
A.错误
B.正确
正确答案:————
25.[判断题] 判断下面命题的真值<img alt="" src="http://file.open.com.cn/itemdb/dbdx/lisanshuxue/test/123068787532812.bmp" />
A.错误
B.正确
正确答案:————
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