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(MATH132)midterm98F.pdf
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Name: ClassSection:
IDNo. TutorialSection:

ProblemNo.1(10)No.2(10)No.3(15)No.4(10)No.5(10)No.6(15)No.7(10)Total Score
1.LetAandBbesets.Pleasecircle\Yes"or\No"forthefollowingstatements:(10pts,each2pts) (a)A[B.A[B YesorNo (b)A[B.A\B YesorNo (c)Thesetofrationalnumbersisuncountable.YesorNo (d)Thesetofrealnumbersbetween0and 0:000000000001iscountable.YesorNo (e)A\(B[C).(A\B)[(A\C)YesorNo
2.Letp,qandrbestatements.Pleasecircle\Yes"or\No"forthefollowingstatements:(10pts,each2 pts) (a)(p!q)$(:p_q)isatautology. YesorNo (b)p^(p!q)!qisatautology. YesorNo (c)(8xP(x))$:(9x:P(x))isatautology.YesorNo (d)(8kP(k)!P(k+1))$(8kP(k))isatautology.YesorNo (e)[((9kp(k))!(8kq(k))]$[8kp(k)!q(k)].YesorNo
98x+668y.58
(15pts)
4.LittleJohngot20HKdollarcoins,allofthemarethesame$1coin.Hehaseightdi.erentpockets.In howmanywaysJohncanputhis20coinsintohiseightpockets.(10pts)
(p)
6.HowmanyarrangementsarethereforthelettersfA.B.C.D.EgsothatAisnotinthe1stposition, Bnotinthe2ndposition,Cnotinthe3rdposition,Dnotinthe4thposition,andEnotinthe5th position.(15pts)
yp(p)