《離散數(shù)》試題及答一選題本共小題每題3分，共15分在小給的個項，有一是合目要的命公式(Q為()(A)矛式(B)可足式(C)重式(D)合范式．設(shè)表“天下大雨示“他在室內(nèi)運(yùn)動命“除非天下大雨，否則他不在室內(nèi)運(yùn)動”符號化為（(A)

Q

；

．

Q

；

(C)．

；

(D)．

Q

．設(shè)合A{6,7,8}}，下式為真的()(A)(B){1,2,3}(C){{4,5}}(D)設(shè)A＝B={ab,c},C={c,},則×B)=)(A){<1,>,<2,c>}(B){<c,1>,<2,>}(C){<,1><,2>,}(D)c,2>}設(shè)G如圖：那么不((A)哈頓圖；(B)完全；(C)歐拉圖；(D)平面二、填空題：本大題共小，每小題分共分。把答案

填在對應(yīng)題號后的橫線上。設(shè)合={}}則A的集(A)=設(shè)合={1,2,3,4},={6,8,12},A到的系R＝{,yy,xy}那么R

＝

，戚_______是等價關(guān)系.寫一個不含“

”的邏輯聯(lián)結(jié)詞的完備集

10.設(shè)X＝{,c}是上二元關(guān)系，其關(guān)系矩陣為01

＝1，么R的系圖為00

三、證題共30分）11.（10分）已知、、三個集合，證明A∩∪C)=(A∩∪∩C)12.（10分）構(gòu)造證明(P(QS))∧∨P)∧RS13.（分）證

[

，

[0,1)

與

[

等勢。四解題共分)（分造三階幻（以1為首的9個續(xù)自然數(shù)正好布滿一個方且方陣中的每一行,每一列及主、副對角線上的各數(shù)之和都相.15.（8分求命公式(

的真值（分設(shè)R是A＝{1,2}到＝(a,b,)的元關(guān)系，是A到A＝{13{<1,a>},R={<,>}2/

}二元關(guān)系，=1

求R集合表達(dá).117.（分）某項工作需要派A、、C個人中的個人去完成，按下面3個件，有幾種派法？如何派？三個條件：(1)去，則CD中去個人；(2)B和不都去；(3)若去則D留下。一單選題每題3分共分)1.B2.C4.A5.B二填題每題分，共20分{,{},{{}},{,{a}}}7.{<6,3>,<8,4>}8.老鄉(xiāng)

c第10題答案圖

{

或

{

或

{

或

{10.見題案11.證明：∵xA（∪C）xA∧∪C）··············································2xA∧（·········································································3（xA∧∨（xA∧···························································5分x∩）∨A∩C··········································································分x∩）∪（∩C）·········································································分∴∩B∪）（∩）（∩）·································································分12.證明）附前提（）PP··················································································分（）T(1)(2)，I··································································分（）(QS)P·················································································4分（）ST(3)(4)，I····································································5分（）P·················································································6分（）T(5)(6)，I··································································分（）S···············································································分13.證：設(shè)

11{,2

1n

,}

，作

f:

如下：··························2分1f()1(),xAnf(xx,(0,1)A

·····································································5分b)設(shè)

1{,2

1n

,}

，作

f[0,1]

如下：·········································7分/

0101

f(0)11(),nnf(x

·····································································10分14.951填對每個格得分。15.P0

(P)

表中最后一列的數(shù)中，每對個數(shù)得2分16.

M

R

1,

分

1

M01R

分M

R

10

10

1

分1

分17.解設(shè)：去工作：去作C：去工作；DD去作。則根據(jù)題意應(yīng)有AD，∧C，必同時成立?！ぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁ?分因此(AC∧B∧)(C)(C∧∨(D∧(∨)∧∨)(C∧∨(D∧∧)∨(∧)∨∧))∧∧)∨(∧∧)∨(∧∨(∧∧)∨(C∧∧∧)∨C∧D∧∧)∨C∧D∧∨(C∧∧)∨(∧D∧∨(∧D∧∧)∨∧D∧)∨(∧D∧∧)∨∨∧∨∨F∨(∧D)∨∨F∨∧D∧)F∨(∧)∨∧)∨(∧∧D∨∧∧)∨(∧)∧)∨(∧∧D∨∧)/

T··················