# Lab 2 solutions - MATH*2000 Fall 2012 Lab #2 Thursday,...

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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.¬XS3.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¬SX. 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 provethatPR,RQ,¬(PQ)¬Pis a valid argument.
29.¬P(FALSE) (from 8 by Complement law)10.¬P(from 9 by Identity law)Problem 0.3.Simplify:1.{xN|x2=x+ 2}. Although both2and-1work,-1/N, thus the answer is just{2}.2.{xN|2x <
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