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1、B卷1．Showthat((pÚq)ÙØp)®qaretautologies.(10scores)2.Supposethatf(x),g(x)andh(x)arefunctionssuchthatf(x)isW(g(x))andg(x)isW(h(x)).Showthatf(x)isW(h(x)).(10scores)3.Letand.FindBtAt.(10scores)4.Findacompatibletotalorderingfortheposet({2,4,6,9,12,18,27,36,48,60,72},
2、).(10scores)5.LetRbetherelatio
3、nonthesetoforderedpairsofpositiveintegerssuchthat((a,b),(c,d))ÎRifandonlyifa+d=b+c.ShowthatRisanequivalencerelation.(15scores)6.UseadjacencymatrixtofindthenumberspathsbetweenU1andU5inthegraphinFigure1oflength3,determinewhetheritisplanarandifitisplanar,intohowmanyregionsdoesthisgraphsplitthep
4、lane?(10scores)7.Supposethereare7finalstobescheduledsothatnostudenthastwoexamsatthesametime.Supposethecoursesarenumbered1through7.Supposethatthefollowingpairsofcourseshavecommonstudents:1and2,1and3,1and4,1and5,2and3,3and4,4and5.Pleaseschedulethefinalexamsforthis.(10scores)8.UsePrim’salgorith
5、mtofindaminimumspannigtreeinthefollowinggraph,thenuseKruskal‘salgorithmtofindaminimumspannigtreeinthesamegraph.(10scores)9.SupposeTisanorderedrootedtree.AndtheinorderlistingofTish,d,b,i,e,j,a,f,c,k,gThepreorderlistingofTisa,b,d,h,e,I,j,c,f,g,kPleasedrawTandfindthepostorderlistingofT.(15score
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