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西南大学19秋[0004] 离散数学在线作业参考

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作业答案 发表于 2019-10-2 09:29:29 | 显示全部楼层 |阅读模式
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2019-10-2 09:29:29 46 0 看全部
0004 离散数学
; P# `/ S. _4 i2 W- `: h* F1.[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(      )
& R: S3 ]6 ^: _奥鹏作业答案可以联系QQ 761296021
, g8 [& o9 y& }7 }" Q. K    A.有零因子环5 f9 e" Z- Y9 l- M% j# X
    B.域和整环
. C# y. F$ x5 X9 d. L    C.整环
$ ?& u3 R9 a5 J/ @6 Z    D.域
3 z/ q# [. @: f( I2.[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(         )7 P% g& K# e' ?* Z2 v) D3 ]% c& P
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463486483099467.png" title="201608291472463486483099467.png" alt="blob.png"/>
* K! g2 a7 U& `  C    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463496691067223.png" title="201608291472463496691067223.png" alt="blob.png"/>1 G7 D& Z+ F7 E$ _9 T
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463472252076958.png" title="201608291472463472252076958.png" alt="blob.png"/>/ }7 C8 N# J- H4 ?, b2 U7 n
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463510500026860.png" title="201608291472463510500026860.png" alt="blob.png"/>
. v1 U3 G6 q, i7 x6 }) Z3.[单选题]设集合A中有4个元素,则A上的等价关系共有(    )个
+ r8 n( s$ u# \5 f6 [    A.14
) F* a: o, K6 C9 L$ o+ ~    B.16- C" o; ^0 I# _1 Z
    C.15+ i  W* V2 O* h$ w) ?) Q9 h
    D.13
: p( {2 {: U- f6 ~0 q4.[单选题]设R í A ′ A,S í A ′ A,则下述结论正确的是(       )$ A: G5 D4 b7 u! \! W5 G
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462307991044238.png" title="201608291472462307991044238.png" alt="blob.png"/>
* w8 q+ o; M8 ~$ _, n& S9 f' e    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462319270022308.png" title="201608291472462319270022308.png" alt="blob.png"/>
2 z% D3 [3 X% W/ y# c    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462328036019244.png" title="201608291472462328036019244.png" alt="blob.png"/>
& g: T* V* `) q% u7 B    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462336998037005.png" title="201608291472462336998037005.png" alt="blob.png"/>4 `; F( B4 H5 W, i5 S
5.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461683092044742.png" title="201608291472461683092044742.png" alt="blob.png"/>
' n$ a4 n" c! `  Q5 }+ _; w, Y    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461731468063560.png" title="201608291472461731468063560.png" alt="blob.png"/>' _" a2 R. L3 t  O
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461763256081655.png" title="201608291472461763256081655.png" alt="blob.png"/>
# e7 R/ I* w* u    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461751665038482.png" title="201608291472461751665038482.png" alt="blob.png"/>" w- M) r1 {$ {/ I
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461740744054269.png" title="201608291472461740744054269.png" alt="blob.png"/>* a. ]5 V9 x0 k$ _8 v, D
6.[单选题]设集合A中有4个元素,则A上的划分共有(    )个4 A, F1 O/ T3 }: L. [8 {# q6 p
    A.15
6 w/ z/ G( A' q    B.14- B: E. j+ w: h, A
    C.13+ @5 L6 _( M- u/ o
    D.16/ ^' H7 W8 c* ~6 O# }7 Y+ u1 _
7.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460659608056015.png" title="201608291472460659608056015.png" alt="blob.png"/>
/ R$ f9 b6 s- p: h    A.B.幂等律
+ P1 ^- R6 e3 x( \) `& f. L    B.交换律" L) Y2 v; I4 A$ ]+ ^) d" G$ q
    C.结合律
( E7 c  t/ R0 }8 n+ \  s  ?    D.消去律" }& [; P: r  t2 n" ^# S
8.[单选题]设集合A中有99个元素,则A的子集有(     )个
  ^  w4 {4 `/ S7 z7 J6 f    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461456245092362.png" title="201608291472461456245092362.png" alt="blob.png"/>
0 R* D- s6 p& N2 L. C    B.100' c+ k- R# v; m( V6 D
    C.99
" ~  ~$ X; D% m+ I    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461470498092835.png" title="201608291472461470498092835.png" alt="blob.png"/>4 L3 r; L' N" q, l
9.[单选题]域与整环的关系为(      )
9 Z! R6 U" x# d. l$ R8 j1 q    A.A. 域是整环
* n8 y: U. ]: c: K; v    B.D.域不是整环
+ K- Z7 G& A4 {9 W: M: `$ D    C.整环不是域
% W+ q1 `% y3 ?    D.整环是域4 l' W  f2 f6 y- ?
10.[单选题]不同构的(5, 3)简单图有(       )个! Y  v/ i0 }. L0 u
    A.2
' S! H/ T, w  ~3 E" H3 H2 U    B.37 u) H4 X& r$ s" {) e4 [' ^2 Q  W
    C.44 i1 l; e7 x/ J& }4 {3 T' l
    D.5
7 X- K% D3 ~; ~: f11.[单选题]下列偏序集,(     )是格% u  p* ?" I& C  k6 f, c
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460902297061420.png" title="201608291472460902297061420.png" alt="blob.png"/>
! m& P, r, B. m$ i5 _' M7 y2 X. B    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460881135064094.png" title="201608291472460881135064094.png" alt="blob.png"/>; ]- ]3 ^2 C8 p7 \
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460893025074066.png" title="201608291472460893025074066.png" alt="blob.png"/>
7 U2 f8 s. X6 q! j. ?% O, w    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460871862004688.png" title="201608291472460871862004688.png" alt="blob.png"/>
* w) x% a9 x3 i& w' y12.[单选题]下列联结词中,不满足交换律的是(     )
) A* M6 t- ~& X+ C% P$ ~( l    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461632550033559.png" title="201608291472461632550033559.png" alt="blob.png"/>. }2 E2 ~6 Q/ B0 Z/ _: J# I2 ?/ k
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461623240005742.png" title="201608291472461623240005742.png" alt="blob.png"/>/ W* _7 `+ i4 f
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461644354046970.png" title="201608291472461644354046970.png" alt="blob.png"/>: Y4 J! ?) j) i; s  d. \: u& r
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461658030042117.png" title="201608291472461658030042117.png" alt="blob.png"/>/ ^8 ?1 g: K. s  a5 R
13.[单选题]设A, B, C是集合,则下述论断正确的是(       )5 i4 A4 h1 s- }
    A.C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462242394070974.png" title="201608291472462242394070974.png" alt="blob.png"/>
  `- D# ?) J# A4 v8 J    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462233426028059.png" title="201608291472462233426028059.png" alt="blob.png"/>
/ l" C, j0 t6 p# g0 h) F    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462223378091131.png" title="201608291472462223378091131.png" alt="blob.png"/>
1 ~5 M9 c- }+ [) t6 @+ t    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462204923046299.png" title="201608291472462204923046299.png" alt="blob.png"/>( A4 X% a- h9 y
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(         ), Y  k& C" a* n. [( `
    A.(1, 1)
+ T1 s1 F' Z  e: G8 G, p4 u+ }    B.(1, 2)
" o! b1 _/ g, _4 B& `2 a  T8 V    C.(1, 3)    微信7612 96021: \. d0 D7 c3 H  f& ?. R4 j
    D.(1, 4)
" j0 h; G1 c9 E2 ^4 Z, t/ M- w- G15.[单选题]具有4个结点的非同构的无向树的数目是(         )
6 G. M  D9 a4 \$ y# I    A.2
/ ]' P; W+ Q, O4 Y+ T2 \% E    B.3
3 U  O) r: b2 Y3 D. p& R$ d* p5 q    C.4
2 Z, q3 G/ b7 p0 [# P    D.52 R1 k& [# `, n$ b4 _8 ?7 i
16.[单选题]设集合A中有4个元素,则A上的划分共有(    )个.
7 \  F  Z5 a- o5 M1 d- _) s    A.13' Y, |5 c- r. c* x
    B.14* Q5 j4 S  u0 Z+ {4 c
    C.15  T9 {# P8 o& s7 {6 O* Y
    D.16
( ^, q- W6 u# S' z& Z17.[单选题]<img title="1460374140461024812.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374140461024812.png"/>
9 Z' Y1 [- @6 c/ z9 M    A.<img title="1460374181655048768.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374181655048768.png"/>5 p( W/ t/ M( `
    B.<img title="1460374210997021639.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374210997021639.png"/>
! Q+ y  o: n7 y. y    C.<img title="1460374237809074307.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374237809074307.png"/>- C$ v/ Y* U# q, O, y
    D.<img title="1460374265630069312.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374265630069312.png"/>
( X& Y- i* y0 n3 V& X18.[单选题]<img title="1460203630269025115.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160409/1460203630269025115.png"/>0 x& v3 f- \+ c" y2 n
    A.偏序关系# ~; `3 ?' W8 r. w0 i- r% {
    B.等价关系
7 ]" e) l. y- s    C.相容关系5 ?+ {  s% I: q4 C2 I6 _
    D.以上答案都不对
* C# ^- a; A( U19.[单选题]<img title="1460366279162057512.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460366279162057512.png"/>, x3 o; k, Y! Q6 Y$ L
    A.偏序# y7 v8 `2 H" a4 y- r, p1 @+ F
    B.等价9 a0 w2 x' \0 @3 q/ j% e
    C.相容
! Z) c( C. v* A# \    D.线性序  M3 h4 I) ?* D, \- d- |8 ?" L
20.[单选题]设集合A中有99个元素,则A的子集有(     )个.4 h% x% f' O3 K* `& R. W
    A.<img title="1460361527937040692.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361527937040692.png"/>( a1 w  i' q/ D! {& W9 y
    B.99
) m5 ]/ _" z& D( q; Y( n% \    C.<img title="1460361570276880171.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361570276880171.png"/>: k1 O8 X8 K9 d9 n5 u; l1 W* L4 b3 v/ V
    D.100
4 y9 y8 D: t# \% U5 B& V* L2 e21.[单选题]设集合A中有4个元素,则A上的等价关系共有(    )个.2 Y0 J+ x* m1 |9 ]$ A9 I
    A.13- X9 ]( M. z' M4 c5 K% y
    B.14
# c0 n& H3 S7 w- S2 [  D/ U& u    C.15' @: X; E3 S& q( L
    D.16
4 d1 j) `! _6 ~& C" o4 A+ q- Q22.[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(         )
7 ~) R) l! V) S4 h    A.自反的- v  z, s5 q' }0 s1 ]  R4 }( Y
    B.对称的
: M5 K1 [! _# `9 t" U4 c    C.传递的、对称的
* v. Y2 Q, b5 }* u: D    D.反自反的、传递的( P2 S" H3 |/ N$ D/ V
23.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460752232008078.png" title="201608291472460752232008078.png" alt="blob.png"/>9 E  |! Z7 X  d, T; f! n$ b
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460805988082806.png" title="201608291472460805988082806.png" alt="blob.png"/>
- |5 C* H6 \1 G2 o9 F    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460821514047196.png" title="201608291472460821514047196.png" alt="blob.png"/>, j, `5 I- O& w9 j2 a) ?% Q
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460791899067229.png" title="201608291472460791899067229.png" alt="blob.png"/>
5 h: y( h3 w* g    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460837925091993.png" title="201608291472460837925091993.png" alt="blob.png"/>; e+ z3 [, s  L
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(     )
# @) l$ k% G; f) z    A.对称的、传递的
. ?0 i7 b5 e8 L6 j( u% x% r    B.反自反的、传递的
% ]/ h( l1 R$ }' [2 l- e    C.自反的
8 G# Y. y# p  w( J' {    D.对称的  }, v: H& {7 Y9 B7 Z
25.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457865087089992.png" title="201608291472457865087089992.png" alt="blob.png"/># [+ E1 f2 C( f- \7 w. x  P# F% v
<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457882427070385.png" title="201608291472457882427070385.png" alt="blob.png"/>6 j) e% v. a; y
    A.F.传递- I3 |/ G; L( Y+ I6 r1 s. q" K
    B.等价- H- L9 c: M& X( m# p
    C.对称! G+ I9 k5 {8 e/ O0 C6 I( |
    D.自反; C, R- \$ o7 i% Y7 f$ m7 S$ a
26.[单选题]在谓词逻辑中,下列各式中不正确的是(     )
% X6 m  |4 D" r3 W  s0 N) Q- [0 {( K7 M5 [  E, @+ u

2 I9 Y, x& C" a    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462394047046361.png" title="201608291472462394047046361.png" alt="blob.png"/>
7 E! L6 e& Q; k2 Q8 p    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462385423040158.png" title="201608291472462385423040158.png" alt="blob.png"/>
7 L. t+ e. ~+ k    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462404417085118.png" title="201608291472462404417085118.png" alt="blob.png"/>. {- ?* E  L0 z9 Z- A% X0 P* H
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462376673085814.png" title="201608291472462376673085814.png" alt="blob.png"/>- R- z; W) I9 x" \: j) v1 ]+ U
27.[单选题]5 x; |: }# a- ]3 k
<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457810380047161.png" title="201608291472457810380047161.png" alt="blob.png"/>; K7 s& _0 q: E# w. y8 b5 P
    A.0
! I' R+ s' c2 j$ C; w    B.x
9 E) Q: V3 }/ O/ Q/ ]+ k    C.y
6 l/ ^8 R/ e8 \( u  H) `9 Z9 D    D.1
/ F* W$ A+ S: D9 t: {( D28.[判断题]任意整数都是0的因数.4 y7 d8 X! L% q# z
    A.正确; i- F3 T1 R$ ~$ G, l* f, g
    B.错误
: A+ ?& N2 w. x5 [9 P) @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________
7 T" f: Y# e; f: y+ }0 P    A.
% M' l" E' E3 L, S; p/ c1 e30.[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9 l" z1 S. z( E5 Z* T4 H; ^
    A.
+ x6 u: S" b1 Q9 W31.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457711547063329.png" title="201608291472457711547063329.png" alt="blob.png"/>
7 c4 {3 E% W* ]' o; n! L    A.
/ U5 Q. h/ t* N32.[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
* }' g# B; O# L, E$ n; T0 g' O    A.
2 a$ \, |2 m% ]) p33.[主观填空题]设集合A = {1, 2, 3},则A上的置换共有(       )个$ {, O6 z. ]$ T- I
    A.
- G2 [' ^+ U' {, O: h34.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463281667027112.png" title="201608291472463281667027112.png" alt="blob.png"/>
1 ~& q4 N. _* \' f- r    A.; I; j4 x3 x8 C) l2 j- T& C
35.[主观填空题]集合A上的等价关系R必满足(       、       、      ); D$ x* M, w8 f/ c. E0 A& S" Z
    A.4 ^% ?- e7 f2 }3 K0 f
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.+ F  y/ |: r3 V; _* k7 t
    A.: N6 ~- f9 ^0 M5 b+ B' u9 _0 d/ e
37.[主观填空题]所有6的因数组成的集合为(        ).
+ O( ]  m( ?# j- n/ q8 M. R; y    A.
, Y# k( L/ s3 J38.[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.
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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 = {___________}.
- S  T" {6 _* m8 i; W    A.  e+ k" P6 R+ c! r$ J) L
40.[主观填空题]有限域的元素个数为(      ), 其中(       )且(           )
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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"/>
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42.[主观填空题](                          )无向图称为无向树.; A/ H1 i" H, p) P, N! J. {
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43.[主观填空题]三个元素集合的划分共有(      )种.9 n; |  U9 ?8 x
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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>_______}.! R+ P8 D7 d0 k) D" `* N
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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"/>/ Z: ]4 z( x2 g1 F' e- s: \* M3 u
    A.
& @' J7 k' ]" G0 J+ Q3 h! \, P46.[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"/>
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0 F3 }2 \: E$ V, X7 `5 _: g6 p4 w47.[主观填空题]集合A上的等价关系R必满足(       、       、      ).4 T6 j8 e& E  L: C  ?
    A.
' z9 w7 t9 x, @' H48.[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"/>5 o9 J/ W: ~; Y6 s
    A.
, }' k1 l& `$ r. {49.[主观填空题]设集合A = {1, 2, 3},则A上的置换共有(       )个.+ a, E6 r" x: s2 ^- E3 z. L, {" W
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50.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463234629093235.png" title="201608291472463234629093235.png" alt="blob.png"/>- Q: u( w1 D3 K* m# F% h
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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(       )* b/ n6 D) W" c  c/ y
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52.[主观填空题]任意6阶群的平凡子群一定是(         )群
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  N; y0 L! L) N+ ~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8 L- [7 D) q( T4 a% W
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54.[问答题]已知A ={{?}, {?, 1}}, B = {{?, 1}, {1}}, 计算A∪B, A+B,A的幂集P(A)
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: n8 n! B! l8 b4 d55.[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.
0 ^" F7 J6 A) U, A* E        (2)画出两棵不同构的满足上述要求的无向树. 3 Y: m3 g4 t& ~& s2 U+ g) b

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    A.
) l! b  E. I' T5 b56.[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?! h: Y# E( c8 R
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    A.
) f1 F5 p0 g- t! v57.[问答题]画出所有不同构的5阶无向树.- I+ \+ Y( a+ j4 H( `
    A.
9 l5 z8 ^/ \" ~& f( A: S9 f% C. S7 k58.[问答题]画出所有不同构的4阶根树.
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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>% i2 u4 l& f9 A: q. e
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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?
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