MATH*2000 Fall 2012 – Lab #2Thursday, September 20Problem 0.1.Test the validity of the following argument:If I study, then I will not fail Math 2000.If I do not play X-box games, then I will study.But I failed Math 2000.Therefore I must have not played X-box games.Proof.LetS= I study,M= I fail Math 2000,X= I play X-box games. Then the aboveargument is as follows1.S⇒ ¬M2.¬X⇒S3.M————————-4.¬XNote that, the contrapositive of (1) isM⇒ ¬S. So, together with (3), we have¬S(thatis,¬Sis true).The contrapositive of (2) is¬S⇒X. Since we know¬Sis true, we haveXis true. But(4) says¬Xis true. SinceX∧ ¬Xis false, the argument is not valid.Problem 0.2.Using the laws of the algebra of propositions and the rules of inference provethatP⇒R,R⇒Q,¬(P∧Q)‘¬Pis a valid argument.
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