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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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0004 离散数学
& Q  h+ l6 p9 [1 E) `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(      )7 V) i' y  d% v( l
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* m. f! l/ g3 ^2 f5 I) m    A.有零因子环
8 d/ B% {* F8 p    B.域和整环
0 y( D% e+ ]' l( b4 T6 J/ E1 A5 @% H    C.整环
" K* S+ l) t/ @/ t    D.域+ K$ @: T3 Y, K+ G6 `
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(         )
1 ^: O& }, F, S0 k% }    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463486483099467.png" title="201608291472463486483099467.png" alt="blob.png"/>
+ w: O9 K/ Q6 [3 q9 l    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463496691067223.png" title="201608291472463496691067223.png" alt="blob.png"/>9 P0 }$ ]6 X" X2 K: w4 t
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463472252076958.png" title="201608291472463472252076958.png" alt="blob.png"/>0 o1 {; D2 A" B" z$ z, \
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463510500026860.png" title="201608291472463510500026860.png" alt="blob.png"/>. t2 C" @( E5 g7 K8 t
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( @! F  t9 z1 m
    A.14
& w" M! e# p5 _6 o4 w( Q    B.16
! x" l  i, S2 D% S  U: w4 T    C.15
8 b$ K& v2 u8 G8 i) [+ _    D.13- ]! ~# ^0 v) Y1 D
4.[单选题]设R í A ′ A,S í A ′ A,则下述结论正确的是(       ). P+ S3 s  h* z( M. C
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462307991044238.png" title="201608291472462307991044238.png" alt="blob.png"/>7 W4 }6 O& F7 g+ c
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462319270022308.png" title="201608291472462319270022308.png" alt="blob.png"/>
* v7 c# b! k* T2 F: }2 Y    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462328036019244.png" title="201608291472462328036019244.png" alt="blob.png"/>- v6 `8 v: o/ C% h) o+ F9 v
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462336998037005.png" title="201608291472462336998037005.png" alt="blob.png"/>, N  g2 A% t& O6 J% d/ P% e7 g
5.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461683092044742.png" title="201608291472461683092044742.png" alt="blob.png"/>& \9 Z# \5 s0 s0 J6 q, [, A8 i$ s6 O
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461731468063560.png" title="201608291472461731468063560.png" alt="blob.png"/>
, c0 C2 v  K8 I1 O6 S  y    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461763256081655.png" title="201608291472461763256081655.png" alt="blob.png"/>
+ |0 H6 S( A) B# a3 R6 ~1 R$ V    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461751665038482.png" title="201608291472461751665038482.png" alt="blob.png"/>0 m; F% O! F  p& W/ Z2 q6 `+ k
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461740744054269.png" title="201608291472461740744054269.png" alt="blob.png"/>
* W( D& I6 }. ]# |, i) y6 F4 w2 x6.[单选题]设集合A中有4个元素,则A上的划分共有(    )个
  Z1 ~! H3 }, x) Y    A.15( R& J$ d9 q' E  N8 T
    B.14# H8 T3 l7 F% C9 A+ ~, p  f, E( p7 }
    C.13
( O: d. l+ G  d0 q% y: C    D.164 {6 F' E8 E3 F% h5 q; F( @5 z
7.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460659608056015.png" title="201608291472460659608056015.png" alt="blob.png"/>7 U0 E0 l* O: f) Q: W# i
    A.B.幂等律" @# s; a$ R$ N- {# K8 a/ ]
    B.交换律( ^  h2 n7 N6 [  ~, ?/ s1 P
    C.结合律" A/ `* }" u6 g2 {) f
    D.消去律
: T0 l0 @1 F0 e/ i1 l; E) F8.[单选题]设集合A中有99个元素,则A的子集有(     )个
; ?1 l) t, W  Y+ i# K    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461456245092362.png" title="201608291472461456245092362.png" alt="blob.png"/>+ @, H. T! e+ L" i8 d8 E- ^6 W
    B.100
, N; ]1 ], p/ i/ C3 B% J+ f1 K    C.99
9 p- C( o. _3 F: F    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461470498092835.png" title="201608291472461470498092835.png" alt="blob.png"/>
+ N9 G* z2 P1 i  N* p4 \9.[单选题]域与整环的关系为(      )
8 x, |) l0 v" l2 Q# D    A.A. 域是整环$ K8 A' z; a7 }4 d: H3 E) v
    B.D.域不是整环
# k: a+ N: Z# Y5 G# x0 q4 Q    C.整环不是域
. Z, g3 ?  D. _2 p" S    D.整环是域% O. [: N  [- f
10.[单选题]不同构的(5, 3)简单图有(       )个
& F& D$ S" O: p* s$ C    A.2, e4 k# `7 c" k
    B.38 @4 |; E) T* M2 [
    C.44 X! Y+ y% i; |; o& |- W
    D.5( y* X+ V6 R9 n, v
11.[单选题]下列偏序集,(     )是格) ~2 k. E; C6 b) m
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460902297061420.png" title="201608291472460902297061420.png" alt="blob.png"/># y( D3 K& @" d2 Y6 s, @6 E7 I
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460881135064094.png" title="201608291472460881135064094.png" alt="blob.png"/>3 d5 w$ q8 l1 L9 s. V
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460893025074066.png" title="201608291472460893025074066.png" alt="blob.png"/>
1 p# x! O; G9 u' m7 L: L    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460871862004688.png" title="201608291472460871862004688.png" alt="blob.png"/>
3 K2 @! w. @- }, A, g12.[单选题]下列联结词中,不满足交换律的是(     )
5 }* y7 _2 y, d! c    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461632550033559.png" title="201608291472461632550033559.png" alt="blob.png"/>  _2 Q7 q! J0 J3 e
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461623240005742.png" title="201608291472461623240005742.png" alt="blob.png"/>' t4 T( o, g& R- \' f; ^* G! e- Q
    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461644354046970.png" title="201608291472461644354046970.png" alt="blob.png"/>5 Q. x' J- F+ D/ u% c1 A9 S
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472461658030042117.png" title="201608291472461658030042117.png" alt="blob.png"/># N6 l) B$ {0 O& F4 v; {2 i
13.[单选题]设A, B, C是集合,则下述论断正确的是(       )# |* c& r5 {9 M4 c1 }8 e
    A.C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462242394070974.png" title="201608291472462242394070974.png" alt="blob.png"/>1 m0 C: L6 q+ d
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462233426028059.png" title="201608291472462233426028059.png" alt="blob.png"/>
' E. I  D5 ]  o    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462223378091131.png" title="201608291472462223378091131.png" alt="blob.png"/>% X& g$ @1 W2 ^9 w# k5 e
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462204923046299.png" title="201608291472462204923046299.png" alt="blob.png"/>/ }! a" s+ l( F6 I; a" J" f7 W
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(         )
' X' [8 O6 u- b    A.(1, 1)* Y# Q; `5 x7 f! B1 {1 \
    B.(1, 2)
3 y5 u/ s) }3 O& l    C.(1, 3)    微信7612 96021
3 u* ?- _. b7 T+ J! t# |    D.(1, 4)
/ {0 ^  o9 G" @$ G( E5 v# P15.[单选题]具有4个结点的非同构的无向树的数目是(         )
# q! h! J) b  k" E- A& o4 Z    A.21 j0 O5 F& b3 U" v) |: ~4 F
    B.3
  d. r# s# H8 d8 ]) X% v8 x    C.4
3 J( g( s+ p; @( o* j    D.5. S' O' O: p% f8 z3 `
16.[单选题]设集合A中有4个元素,则A上的划分共有(    )个.) X, U6 {! r* s" e* F7 A! r
    A.13% ~5 s6 I9 P4 e/ I# }2 l
    B.14; t5 [: f) y7 Y: c
    C.15
, {1 s9 U+ k6 p+ L: D. [    D.16
; }- c  L; O; U" ?3 o+ v2 _17.[单选题]<img title="1460374140461024812.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374140461024812.png"/>0 A) y5 ^, Q) }5 U
    A.<img title="1460374181655048768.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374181655048768.png"/>
# j2 \+ _2 T' |/ F  f$ ~    B.<img title="1460374210997021639.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374210997021639.png"/>
# u  F$ I& p7 {$ |: I9 j5 @    C.<img title="1460374237809074307.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374237809074307.png"/>. s; |/ G0 x! t. P  j7 N- ?6 R
    D.<img title="1460374265630069312.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460374265630069312.png"/>
! ]" w/ P0 o7 V. l18.[单选题]<img title="1460203630269025115.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160409/1460203630269025115.png"/>- I/ r7 c: Q( ?2 T' L: r6 k- t
    A.偏序关系, S9 b* ~0 Z* q$ E# ]
    B.等价关系
* [& L: X; \* ^. Z0 Q( e8 W! |    C.相容关系
# J8 r2 A0 A- D6 H, g    D.以上答案都不对, M% A6 M/ z( c& A# L
19.[单选题]<img title="1460366279162057512.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460366279162057512.png"/>
6 B; ?: N) A3 J9 P; o9 n" V! \    A.偏序
, _' n0 G  }( t    B.等价
& S/ S( W  `) U' @' l' A8 u    C.相容5 r4 k, {- S: z
    D.线性序
, M6 y! }8 C' W- e20.[单选题]设集合A中有99个元素,则A的子集有(     )个.8 @. v6 D0 m4 n& q3 S' [
    A.<img title="1460361527937040692.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361527937040692.png"/>
/ Y! p1 V1 \6 s/ N8 F1 ~6 t) N    B.994 J0 N% A# T! L0 \8 Q4 [' R
    C.<img title="1460361570276880171.png" alt="1.png" src="http://zuoye.eduwest.com/resourcefile/bdeditor/xndx/upload/image/20160411/1460361570276880171.png"/>
) z3 D! L( Y* r/ C: M9 v    D.100
% T1 c. s, T1 B4 l% Y; 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.. F2 ~4 }, l) f
    A.13/ x! S5 @9 j, A' i/ Z! Y: l
    B.14
" P$ Y9 @4 A: d" ?: ]$ x. \    C.15
/ N) F) A" K: m: t    D.165 E& x+ J  l# D1 S0 T5 Q. J- N
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(         )1 C5 r7 |4 d3 ?; t! L$ G
    A.自反的
$ j  y1 Z- ?& J    B.对称的
! g1 S* ?5 `) e$ y- _9 {    C.传递的、对称的, a- I# ]9 [$ h; o" o  x0 W
    D.反自反的、传递的0 E- P. l9 ]# u. ^
23.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460752232008078.png" title="201608291472460752232008078.png" alt="blob.png"/>) \% D7 ?4 Q8 M
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460805988082806.png" title="201608291472460805988082806.png" alt="blob.png"/>% g, }% q( d; {4 |$ x" J
    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460821514047196.png" title="201608291472460821514047196.png" alt="blob.png"/>
  I, c4 ?1 z; d; ~( b* e    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460791899067229.png" title="201608291472460791899067229.png" alt="blob.png"/>1 D+ e& K! c8 z0 D* Z. n
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472460837925091993.png" title="201608291472460837925091993.png" alt="blob.png"/>. U+ ?+ N4 h" Q
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(     )
- M# S; }% g3 V- [    A.对称的、传递的1 h$ \2 g8 x) D3 f) H/ ]
    B.反自反的、传递的% ]+ [0 M( T. U6 F
    C.自反的
' \+ ?  I1 y; P: e" I& F& h: k' P    D.对称的
: t6 b7 F0 B3 D25.[单选题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457865087089992.png" title="201608291472457865087089992.png" alt="blob.png"/>
( s1 V4 r, T1 [6 G2 ?<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457882427070385.png" title="201608291472457882427070385.png" alt="blob.png"/>
0 Q3 W5 }/ N% D6 r* d/ q. V    A.F.传递
0 a: n2 i! x2 T- z" L    B.等价
" ^3 u( m0 x' \) v- D    C.对称+ J4 r1 j. d1 V8 R' a, q
    D.自反6 v6 v& C3 @$ f9 k( q' q
26.[单选题]在谓词逻辑中,下列各式中不正确的是(     )
" P8 }, A+ ?; M* s& ^- L. d% {- B$ A) V, a1 M) v
5 C$ N/ i; |* Z6 o( E9 b
    A.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462394047046361.png" title="201608291472462394047046361.png" alt="blob.png"/>
  m& |% x) U  G* [. g/ M  L    B.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462385423040158.png" title="201608291472462385423040158.png" alt="blob.png"/>
) a, b. g* N  u    C.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462404417085118.png" title="201608291472462404417085118.png" alt="blob.png"/>+ f- B3 v  X" d" E( H
    D.<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472462376673085814.png" title="201608291472462376673085814.png" alt="blob.png"/>
$ ]" L6 e8 s/ x1 n27.[单选题]
/ l  a( X9 H1 X<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457810380047161.png" title="201608291472457810380047161.png" alt="blob.png"/>
- x, a' E8 u* T3 b0 `2 k8 `; L    A.09 |- p$ o0 r: \9 m; H4 B
    B.x7 t: v+ f; W# I6 T9 I/ r$ i
    C.y
9 c: F4 E% }. O% U0 s4 N" Z    D.1- M% g5 ?3 L% I0 i7 W+ a6 y
28.[判断题]任意整数都是0的因数.
* I% @; Y+ ?, V    A.正确
. t) Q- N7 Z% e/ Y2 u& y    B.错误9 W( J5 d7 B- _7 {
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________
$ C; X1 Z0 E: r& A* l. \    A.: l' s, _* n! ~! D
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# O, D" w  f  Y% ?6 m
    A.
2 [# n* @$ a) q$ |: f31.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472457711547063329.png" title="201608291472457711547063329.png" alt="blob.png"/>
  T+ T7 A2 B! U    A.
! c0 `2 a8 x  n# b1 g2 x32.[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8 G5 \; ?% {- A( v9 E8 H. ~/ H2 F
    A.
. r! {$ |4 j! f' ]# G) j6 c33.[主观填空题]设集合A = {1, 2, 3},则A上的置换共有(       )个
% x* m6 B6 n; _+ I    A.& B( u- ^" [. u% f
34.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463281667027112.png" title="201608291472463281667027112.png" alt="blob.png"/>
0 p8 L& A5 [/ o+ D8 c, J    A.3 |3 }( F( k  l1 g" {( @9 _
35.[主观填空题]集合A上的等价关系R必满足(       、       、      )) o- W  q6 b+ Q. F
    A.- S6 n7 x2 Q2 K2 Z9 h( g/ K
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.
( t* W2 }$ X9 c, n! v: I3 G/ l. {    A.
$ H% b7 Z) j( d$ ~4 ?" }37.[主观填空题]所有6的因数组成的集合为(        ).
* F3 ~: A% ?; M; C# Z    A.+ k, x% k. k+ B1 q# ~4 P1 n( h
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.$ H1 Q# v9 p/ T# b" ^; p

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7 {% X- F4 ~* W1 l3 Q  |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 = {___________}.
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40.[主观填空题]有限域的元素个数为(      ), 其中(       )且(           )0 {$ B3 ]% c% _2 i; t, L; Z
    A.
( L, Y4 @2 Q5 k3 F41.[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"/>  B! p. g$ d/ g$ q4 Z8 f8 @
    A.
/ N# w4 N) |: ?% j* u# k42.[主观填空题](                          )无向图称为无向树.% A* n1 x5 d+ l
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3 L5 K3 m. ]: n+ H- \% H' G44.[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>_______}.& L2 f& B% N" T! q7 G! a: E
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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"/>
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. z! z: c' m2 l% @7 s46.[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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47.[主观填空题]集合A上的等价关系R必满足(       、       、      ).
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$ F! O4 L: W4 ]& m0 b48.[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"/>
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6 C8 ^5 [8 v$ f* ?2 B' v  O# P49.[主观填空题]设集合A = {1, 2, 3},则A上的置换共有(       )个.& h3 A5 ?6 ^  N4 ]& G. W
    A.
. ]" `, X" ]1 E4 c/ }8 p/ x50.[主观填空题]<img src="http://zuoye.eduwest.com/resourcefile/uploadFiles/file/questionImgs/201608291472463234629093235.png" title="201608291472463234629093235.png" alt="blob.png"/>
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7 a3 s/ _' p7 e# }! i51.[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(       ). ?! B6 G/ E% \2 e5 ^7 X9 a, s' o
    A.
4 G' z- X9 Z4 e6 [% s( c52.[主观填空题]任意6阶群的平凡子群一定是(         )群4 y1 q3 J6 h# U% L6 D. G5 b
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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- t! ?& w' U& v( J+ R$ R! u
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- D; M7 u; O" D$ g54.[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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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.
4 a+ A$ h: O2 z# ], m' V6 z' f        (2)画出两棵不同构的满足上述要求的无向树.
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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?
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6 ^! @$ P6 \0 i: Z  a$ _57.[问答题]画出所有不同构的5阶无向树./ Q# G% P( N4 A8 f  h* a0 l
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58.[问答题]画出所有不同构的4阶根树.
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5 z6 v2 w9 T- ~8 ^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>% T* o( N2 d; w1 K/ H. V6 Y" s5 |
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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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