···········································································································装订线··································································································山东建筑大学试卷共4页第1页2009至2010第1学期课程名称离散数学A试卷A（A、B）专业：信息与计算科学考试性质：闭卷考试时间120分钟题号一二三四五总分分数一、填空题（每小题2分，共30分）1.Letp:Iwillstudydiscretestructures;q:Iwillgotoamovie.Writethefollowingstatementintermsofp,qandlogicalconnectives.“IwillgotoamovieonlyifIwillnotstudydiscretestructures.”________________2.LetR(x,y):x+yiseven.Thevariablesxandyrepresentintegers.Thetruthvalueofthestatement“xyR(x,y)”is____________.3.LetA={1，2，…，10},definearelationRonAbyaRbifandonlyif|a-b|2(a,bA),determinewhetherRistransitive.4.LetA={1,2,3},R={(1,2),(3,3)}bearelationonA,thenthereflexiveclosure(自反闭包)ofRis____________________.5.LetA={3,7,11},definearelationRonAbyxRyifandonlyifx-y<3.LetMR=(mij)bethematrixoftherelationR,thenm12=,m33=.6.DeterminewhetherthelatticeshowninFigure1iscomplemented(有补的)._______7.InaposetwhoseHassediagramshowninFigure2,thegreatestlowerbound(最大下界)ofB={d,e,f}is.8.LetnbeapositiveintegerandletDnbethesetofallpositivedivisorsofn.ThenDnisalatticeundertherelationofdivisibility.DeterminewhetherD42isaBooleanalgebra._________.9.LetA={1,2,3,4},R={(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4)}beanequivalencerelationonA,thentheequivalenceclass[1]=_________.10.GiventheBooleanfunctiondescribedbythelogicdiagraminFigure3.___________________11.UsetheHuffmancodetreeinFigure4todecodethemessage0111001101(用图4中的Huffman编码树，译出信息0111001101)________________.12.WhetherthegraphshowninFigure5hasanEulercircuit?.13.LetS={1,2,3},forP(S),*isdefinedasintersection,then(P(S),*)isamonoid,andtheidentityis________________.14.IfSisanonemptyset,forA,BP(S),*isdefinedasA*B=AB(symmetricdifference),then(P(S),*)isagroup,andtheinverseofAis_________.15.LetA={Ø,a,{b,c，d}}beaset,thenthecardinality|A|=_______.二、选择题(每小题2分，共20分)在每小题列出的四个选项中只有一个选项符合题目的要求，请将其代码填写在题后的括号内。1.Inthefollowingstatements,whichistrue?()A.3isevenor–2isnotnegative.B.3isoddand–2isnotnegative.C.3isoddor–2isnotnegative.D.3isevenand–2isnegative.2.Whentheproposition(pq)risfalse?()A.p=0,q=1,r=1B.p=1,q=0,r=0C.p=1,q=1,r=1D.p=0,q=0,r=0班级______________姓名______________学号______________山东建筑大学试卷共4页第2页3.LetA={a,b,c,d},whichofthefollowingisapartition(划分)ofA?()A.{{a,b},{d}}B.{{a},{c},{b,d}}C.{{a},{b,c},{c,d}}D.{{a},{b},{c},{d},{}}4.LetA=Z+,definedarelationRonAbyaRbifandonlyif|a-b|3,whichistrueforR?()A.RisreflexiveB.RisantisymmetricC.RistranstiveD.Risasymmetric5.LetR={(1,1),(2,2),(3,3)}bearelationonasetA={1,2,3},whichisthebestforR?(哪一项最适合R)()A.RistransitiveB.RisreflexiveandsymmetricC.RissymmetricandtransitiveD.Risanequivalencerelation6.Inthefollowing,whichstatementistrue?()A.Aposethasagreatestelement.B.AposethasamaximalelementC.Aposethasatmostoneleastelement.D.Noneaboveistrue.7.IntheFigure6,whichisnotalattice?()8.IntheBooleanalgebraD70,thecomplement(补元)of7is()A.35B.10C.5D.2...