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(MATH132)midterm99F.pdf
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ProblemNo.1(12)No.2(12)No.3(12)No.4(10)No.5(10)No.6(12)No.7(12)Total(80) Score 1.LetAandBbesets.Pleasecircle\Yes"or\No"forthefollowingstatements:(12pts,each2pts) (a)A[B.A\B YesorNo (b)A[B.A\B YesorNo (c)(A\B)[(A\B).A[B;A\BYesorNo (d)Countablesetsarein.niteYesorNo (e)A[(B\C).(A[B)\(A[C)YesorNo (f)In.nitesetsareuncountable.YesorNo 2.Letp,qandrbestatements.Pleasecircle\Yes"or\No"forthefollowingstatements:(12pts,each2 pts) (a)(p!q)^(q!r)!(p!r)isatautology.YesorNo (b)(p!q)$(:q!:p)isatautology. YesorNo (c)p^(p!q)!qisatautology. YesorNo (d)(8xP(x)_Q(x))!(8xP(x))_(8xQ(x))YesorNo (e)(9xP(x)^Q(x))$(9xP(x))^(9xQ(x))isatautology.YesorNo (f)(8kP(k))!(8kP(k)!P(k+1))isatautology.YesorNo
3.Findallintegersolutionsforthefollowingequation 98x;68y.38 (12pts) 4.Showthatamongany52integersthereareatleasttwonumberswhosesumordi.erenceisamultipleof 100.(10pts) 5.Vivianwillbuy10pencilsfromastorewhere4typesofpencilsareprovided.Howmanypossibleways forViviantoselect10pencilsfromthestore.(10pts)
1
7.12di.erentsizecolormarblesareusedtomakeanecklace.thereare3di.erentcolorsandeachcolorhas 4marbles.Howmanypatternscanbemadesothatthemarblesofthesamecolorarenotalltogether. (12pts)
2