电大本科离散数学期末复习考试小抄

电离散数学复资料考试抄

单项选择题（题3分题15分）
1．集合A{12}B{12{12}}列表述正确( A )．
A． AÌBAÎB B．BÌAAÎB C．AÌBAÏB D．AËBAÎB
2．设图（a）（b）（c）（d）图示列结成立 ( D )．


图
A．（a）强连通 B．（b）强连通
C．（c）强连通 D．（d）强连通
3．设图G邻接矩阵

G边数( B )．
A．6 B．5 C．4 D．3
4．简单图G棵树仅( A )．
A．G连通边数结点数少1 B．G连通结点数边数少1
C．G边数结点数少1 D．G中没回路．
5．列公式 ( C )重言式．
A．ØPÙØQ«PÚQ B．(Q®(PÚQ)) «(ØQÙ(PÚQ))
C．(P®(ØQ®P))«(ØP®(P®Q)) D．(ØPÚ(PÙQ)) «Q
6．设A{a b}B{1 2}R1R2R3AB二元关系R1{ }R2{ }R3{ }（ B ）AB函数．
A．R1R2 B．R2
C．R3 D．R1R3
7．设A{1 2 3 4 5 6 7 8}RA整关系B{2 4 6}集合B元元界界次 ( B )．
A．8282 B．22
C．6262 D．8161
8．集合A元素数10幂集元素数（ A ）．
A．1024 B．10 C．100 D．1
9．设完全图Kn结点(n≥2)m条边（ C ）时K中存欧拉回路．
A．m奇数 B．n偶数
C．n奇数 D．m偶数
10．已知图G邻接矩阵

G（ D ）．
A．5点8边 B．6点7边
C．6点8边 D．5点7边
11完全图K3构生成子图数（ C ）
(A) 6 (B) 5
(C) 4 (D) 3
12 n阶完全图Kn中边数（ A ）
(A) (B) (C) n (D)n(n+1)
13图G＝中结点总度数边数关系( C )
A deg(vi)2½E½ (B) deg(vi)½E½
C D

二填空题（题3分题15分）
1．命题公式真值　 1 　．
2．A{12}R{|xÎA yÎA x+y<4}R反闭包 {<11><22><12><21>} ．
3．已知棵树T中8结点4度3度2度分支点T树叶数 5 ．
4．(x)(P(x)→Q(x)∨R(xy))中变元 R(xy )中y ．
5．设集合A＝{ab}集合A幂集 {Æ{ab}{a}{b }}
6．果R1R2A反关系R1∪R2R1∩R2R1R2中反关系 2 ．
7．设图G6结点连通图结点总度数18G中删 4 条边变成树．
8．图G存欧拉回路仅G结点度数全偶数 连通
9．设连通面图G结点数5边数6面数 3 ．
10．设体域D＝{a b}谓词公式(x)A(x)∧（x）B（x）消量词等值式 (A (a)∧A (b))∧(B（a）∨B（b）) ．
三逻辑公式翻译（题6分题12分）
1．语句雪黑色．翻译成命题公式．
设P：雪黑色 （2分）
命题公式：P．
2．语句学校．翻译成命题公式．
解：设P：学校
命题公式： Ø P．
3．语句王学生李职员张军．翻译成命题公式．
设P：王学生Q：李职员R：张军． （2分）
命题公式：P∧Q∧R．
4．语句果天参加活动明天会议取消．翻译成命题公式．
解：设P：天参加活动
Q：明天会议取消
命题公式： P® Q．
5．语句旅游仅时间．翻译成命题公式．
解：设 P：旅游Q：时间
命题公式： P ®Q．
6．语句41次列车午五点开者六点开．翻译成命题公式．
解：设P：41次列车午五点开Q：41次列车午六点开 （2分）
命题公式：（P∧ØQ）∨（ØP∧Q）
7．语句张学努力王取成绩．翻译成命题
设P：张学努力Q：王取成绩 （2分）
命题公式：PÙQ．
8．语句课． 翻译成谓词公式．
解：设P(x)：xQ(x)：x课 （1分）
(x)(P(x) ÙQ(x)
9．语句学努力．翻译成命题公式．
解：设P(x)：xQ(x)：x学努力
x）(P(x)®Q(x))．

四判断说明题（题7分题14分）判断列题正误说明理．
1．设集合A{1 2 3 4}B{2 4 6 8}判断列关系f否构成函数f：说明理．
(1) f{<1 4> <2 2> <4 6> <1 8>} (2)f{<1 6> <3 4> <2 2>}
(3) f{<1 8> <2 6> <3 4> <4 2>}．
答：（1）构成函数 没定义构成函数
（2）构成函数 没定义构成函数
（3）满足 意结果唯
2．集合A {123}二元关系R{<1 1><2 2><1 2>}
(1) R反关系 (2) R称关系．
答：（1）错误 R反
（2）错误 R称
3．果R1R2A反关系判断结：R11R1∪R2R1∩R2反 否成立？说明理．
答：成立 意
R11R1∪R2R1∩R2反
o
o
o
o
a
b
c
d
图
o
o
o
g
e
f
h
o
4．偏序集哈斯图图示
集合A元a元存．
答：错误集合A没元没元
中a极元



5．偏序集哈斯图图示集合A元a元存．

解：正确
集合A意元素x均ÎR（xRa）a集合A中元．元定义集合A中存元．
6．果图G图结点度数均偶数图G存条欧拉回路．．
答：错误 果图G图图G连通时结点度数偶数

7．设G连通面图6结点11条边G7面．
答案：正确
定理连通面图G结点数v边数e面数r欧拉公式ve+r2成立
r2v+e26+117
G存条欧拉回路
8．设G6结点14条边连通图G面图．
解：错误满足设Gv结点e条边连通简单面图v≥3e≤3v6． 9．命题公式ØPÙ(P®ØQ)ÚP永真式．
解：正确 真值表
P
Q
ØP
ØQ
P®ØQ
ØP∧(P→ØQ)∨P
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
知该命题公式永真式．

五．计算题（题12分题36分）
1．设集合A{a {b} c}B{{a} c}试计算
（1）（A∩B） （2）（B A） （3）（A∩B）×B．
解（1）（A∩B）{c}
（2）（B A）{{a}}
（3）（A∩B）×B{ < cc >}
2．设A{0123456}R{|xÎAyÎAx+y<1}S{|xÎAyÎAx+y£3}试求RSR·SR1S1r(R)．
解：R{<00>}
S{<00><01><02><03><10><11><12><20><21><30>}
R·S{<00><01><02><03>}
R1{<00>}
S1 S ）
r(R)IA．
3．图G中V{ a b c d e}E{ (a b) (a c) (a e) (b d) (b e) (c e) (c d) (d e) }应边权值次21236145试
（1）画出G图形
（2）写出G邻接矩阵
（3）求出G权生成树权值．

解：（1）G图形表示：

（3分）
（2）邻接矩阵：
（6分）
（3）粗线表示生成树

权7：
4．设图GV{ v1v2v3v4v5}E{ (v1 v2)(v1 v3)(v2 v3)(v2 v4)(v3 v4)(v3 v5)(v4 v5) }试
(1) 画出G图形表示
(2) 求出结点度数
(3) 画出图G补图图形．
v1
v2
v3
v4
v5
o
o
o
o
o
解：（1）关系图






（2）deg(v1)2 deg(v2)3 deg(v3)4
deg(v4)3 v1
v2
v3
v4
v5
o
o
o
o
o
deg(v5)2
（3）补图



5．设集合A{1234}R{|x yÎA|xy|1xy0}试
（1）写出R序表示
（2）画出R关系图
（3）说明R满足反性满足传递性．
解（1）R{<11><22><33><44><12><21><23><32><34><43>} （3分）
°
°
°
°
1
2
3
4
（2）关系图






（3）<11><22><33><44>均属RA元素构成序均R中RA反
<23><34>属R<24>属RRA传递
6．设集合A{1 2 3}R{<11> <21><31>}S{<12> <22>}试计算
（1）R·S （2）R 1 （3）r（R）．
解： （1）R·S {<12> <22><32>} （4分）
（2）R 1{<11> <12> <13> } （8分）
（3）r（R）{<11> <22> <33> <21><31>}

7求出图示赋权图中生成树（求写出求解步骤）求生成树权．
解 Kruskal算法求产生生成树．步骤：
选
选
选
选
选
选 （6分）
生成树图四示：
（9分）
图四
生成树权：w(T)22+1+4+9+3+1857． （12分）

8．试画棵带权2 3 3 4 5优二叉树计算该优二叉树权．
o
o
o
o
o
o
o
o
o
2
3
3
4
5
5
10
7
17
解： 优二叉树图二示．




（10分）
图二
权2´3+3´3+3´2+4´2+5´239
9．设谓词公式试
（1）写出量词辖域 （2）指出该公式变元约束变元．
（1）x量词辖域 （2分）
z量词辖域 （4分）
y量词辖域． （6分）
（2）变元中y中z （9分）
约束变元中x中z中y．
10．设谓词公式试
（1）写出量词辖域 （2）指出该公式变元约束变元．
（1）x量词辖域 （3分）
z量词辖域 （6分）
（2）变元公式中y中x （9分）
约束变元xz．
11．求命题公式(PÚQ)®(RÚQ) 析取范式合取范式．
解：
P
Q
R
PÚQ
RÚQ
(PÚQ)®(RÚQ)
极项
极项
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
ØPÙØQÙØR
ØPÙØQÙR
ØPÙQÙØR
ØPÙQÙR

PÙØQÙR
PÙQÙØR
PÙQÙR




ØPÚQÚR

析取范式（极项析取）：
（ØPÙØQÙØR）Ú（ØPÙØQÙR）Ú（ØPÙQÙØR）Ú（ØPÙQÙR）
Ú（PÙØQÙR）Ú（PÙQÙØR ）Ú（PÙQÙR）
合取范式（极项合取）：ØPÚQÚR
12．求（P∨Q）→（R∨Q）析取范式合取范式．
解：（P∨Q）→（R∨Q）
ÛØ（P∨Q）∨（R∨Q） （4分）
Û(ØP∧ØQ)∨（R∨Q）
Û(ØP∨R∨Q)∧(ØQ∨R∨Q)
Û(ØP∨R∨Q) 析取合取范式
六证明题（题8分）
1．试证明集合等式AÇ (BÈC)(AÇB) È (AÇC)．
证明：设SA∩(B∪C)T(A∩B)∪(A∩C) x∈Sx∈Ax∈B∪C x∈Ax∈B x∈Ax∈C
x∈A∩B x∈A∩C x∈TSÍT．
反x∈Tx∈A∩B x∈A∩C
x∈Ax∈B x∈Ax∈C
x∈Ax∈B∪Cx∈STÍS．
TS．

2．试证明（x）（P（x）∧R（x））Þ （x）P（x）∧（x）R（x）．
证明：
（1）（x）（P（x）∧R（x）） P
（2）P（a）∧R（a） ES(1)
（3）P（a） T(2)I
（4）（x）P（x） EG(3)
（5）R（a） T(2)I
（6）（x）R（x） EG(5)
（7）（x）P（x）∧（x）R（x） T(5)(6)I
请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄The battle for young viewers CCTV is embracing Internet culture and working with independent producers on TV shows to woo audiences under 35 Han Bing bin reports After charming audiences with his warm smile for 14 years China Central Television host Li Jiaming recently found himself targeted by a group of young netizens unhappy with his style The complaints came after Li hosted the premiere of Rising Star on Oct 31 It is a singing competition show that originated in Israel Many young netizens found his hosting style slow and boring and mocked it as CCTV evening gala style They even initiated an online campaign to replace him The 40yearold host＇s reaction to the criticism was surprising During the second episode he jokingly called himself the slow Jiaming and acted much younger talking faster and louder It＇s like selling a product When the customers file a complaint you must change says Li In the Internet age you get feedback very quickly These young people are so cute When you＇re willing to change for them they will quickly like you back In order to win more young viewers CCTV is relying on programs such as Rising Star to embrace Internet culture In Rising Star a studio audience and fans watching on television vote for their favorite singers in real time using the instantmessaging app WeChat Rising Star was designed to be a live broadcast but the Chinese version isn＇t because of policy reasons Still WeChat votes by viewers at home are still a major factor in determining which contestants advance to the next round In the show＇s latest episode more than 65 million votes were cast via WeChat Now the competition among entertainment shows is very fierce Audiences have more diverse needs CCTV needs to embrace an open attitude interact with young audiences and blend with the Internet says Lyu Yitao director of CCTV＇s entertainment channel The producer of Rising Star Enlight Media says the program will have a phenomenal effect given CCTV＇s audience base nationwide But it comes with a challenge says Zhang Hang chief producer of the program and CEO of Enlight Media＇s TV business Unlike topranking provincial satellite channels such as Hunan TV which have a large base of young fans thanks to a series of phenomenally popular entertainment and reality shows CCTV productions are usually more conservative and serious and thus have a much older audience base If we were to run this program on Hunan we may attract twice as many viewers says Zhang But since we didn＇t make it there we now have to make the best out of the given conditions And it means we have to make certain compromises When the current season of Rising Star ends Zhang says his company will conduct an overall evaluation of the program and make adjustments for future seasons Although audience ratings haven＇t lived up to Zhang＇s expectations he says the program has already helped CCTV attract more young people According to Enlight Media the number of people ages 15 to 35 who watched the first episode of Rising Star was 76 percent higher than the usual audience for CCTV entertainment productions In order to attract young audiences CCTV has been working with independent production companies As one of CCTV＇s closest partners Enlight Media has produced several entertainment and reality shows for the company＇s channels including the Chinese version of The Biggest Loser on CCTV＇s business channel and an original teenager talent show Shaonian Zhongguo－qiang (Strong Young Chinese) on CCTV1 This year CCTV also licensed EEMedia the producer of the popular Super Girl talent shows to produce the talk show Hi 2014 hosted by Taiwan pop star Harlem Yu and one of China＇s most popular TV stars Xie Na The show is geared toward younger audiences Canxing Productions which rose to fame with the success of its Voice of China series on Zhejiang TV also produced two talent shows for CCTV One is an original production called Songs of China which ended up as one of CCTV＇s most watched programs of 2014 The State Administration of Press Publication Radio Film and Television announced earlier this year that starting in 2015 only one music talent show can be aired nationwide during prime time each season and there can be only one program based on foreign formats each year However domestic media report that such policies don＇t apply to CCTV meaning it will become a highly desired platform by production companies Wang Changtian CEO of Enlight Media confirmed to the Shanghai Securities News that its programs scheduled to air on CCTV next year which include at least two reality shows won＇t be affected A kung futhemed reality show produced by Canxing is also reportedly scheduled to run on CCTV next year CCTV is very active The level of its acceptance of new ideas is even beyond my imagination says Zhang Hang Our cooperation with CCTV will surely continue When winter comes nothing is more relaxing than a hot spring bath For thousands of years natural mineralrich hot spring baths have also been used to relieve health ailments The water found in natural hot springs contains a variety of different minerals and the most common one is sulfur It has a rotten egg smell but is excellent for skin The sulfurcontaining water might be just what the doctor ordered when it comes to relieving pain stress itchy skin arthritis and more Hot springs resorts are thriving as biting cold winter arrives Here we take a look at some of the best natural hot springs China has to offer


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