離散數(shù)學考試試卷

PAGE第1頁共4頁學院：專業(yè)班級：姓名：學號：裝訂學院：專業(yè)班級：姓名：學號：裝訂線《離散數(shù)學》試卷（A卷）考試形式:閉卷筆試，2小時適用專業(yè)：網(wǎng)絡工程、計算機、通信工程專業(yè)題號一二三四五六總分得分得分評閱人一、選擇題：（10小題，每題2分，共20分）1.Whichofthefollowingarestatements?（）。(a).Is2apositivenumber?(b).(c).Studylogic(d).Shanghaiisalargecity2.Whichofthefollowingistrueproposition?（）。(a).If2+2=4,then2+4=8 (b).If2+3=5,then3+3=7(c).IF2+2=5,then3+3=63.Whichofthefollowingrelationsarefunctions（）。 (a). (b).(c).4.LetIbethesetofintegers，Whichofthefollowingalgebraicsystemarenotsemigroupsfortheoperator*（）①a*b=lcm（a，b），②a*b=a×b③a*b=a＋b，④a*b=a-b.5.Whichofthefollowingisonetoone?（）6.UseI,Q,Rtodenotethesetofintegers,rationalandrealrespectively,whichoffollowingaregroups?(a).(b).(c).（d）.Where=7.Whichofthefollowingiscyclicgroup?()。(a).(b).(c).8.LetA={1,2,…,10},whichoffollowingareclosedonA()。(a).(b).(c).(d).9.LetA={a,b},whichofthefollowingtablesdefineamonoidonA()。*ab*ab*abaabaababababbbbbab(a)(b)(c)10.Letbeaalgebraicstructure,ifthereisaelementeinAsothatforanya∈Athenwecallea()(a)semigroup(b)monoid(c)group（d）identityelement得分評閱人二、填空題：（10空，每空2分，共20分）1.LetA={a，b，c}and,findr(R),s(R)andt(R).r(R)=s(R)=t(R)=2.Completethefollowingtabletoobtainasemigroup.*abcacabbabcca3.Let（G，*）beagroup，ifforanya,binGtheidentitya*b=b*aholdsthen（G，*）iscalleda()．4.DefinethefunctionfandgthatmapRintoRbythen=（），=（）。5.Let（G，*）isagroup,ifGisafinitesetthen|G|iscalled()6．Let（G，*）isagroup，ifthereisasuchthatforanyainGthen（G，*）iscalleda(),andfora∈GthereexiststhesmallestintegernsothatwhereeistheidentityelementofG,wecallthenis()得分評閱人三、翻譯題：（4小題，每題5分共20分）Writethefollowingstatementsusinglogicalconnectives(1)Itisnotcasethateverypeopleknowsmusic(2)Allpeoplelikesports(3)Forallintegersthefollowinginequalityholds:(4)Foranynaturalnumberxthereisauniquenaturalnumberysuchthaty=x+1.得分評閱人四、證明題：（1題10分3、4題各5分，共20分）1．Letbeaalgebraicstructure,the*isabinaryoperationonRthatdefineasfollows（4分）。Showthatisamonoidand0isaidentityelementof2．Letbeacompositionfunctionandbeonto,provethatisonto（4分）3.Provethatisacyclicgroupwhere得分評閱人五、綜合題：（1,2小題8分，3小題4分共20分）Wehavetheposet=wherem|nmeansmdividesn.(a)DrawHassediagramfortheposet.（分）(b)LetB={2,3,4},findthemaximalvaluesofBandminimalvaluesofB.2.LetS={1,2,3}andR={(2,1),(2,3),(3,2)}.(