# Discrete Structure lecture_2

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 2TRUTH TABLEKHAWAJA TARIQ MAHMOODLecture # 2TRUTH TABLECONSTRUCT TRUTH TABLE:1. (pq) ~ (pq)PTTFF(pq)TTTFqTFTF(pq)TFFF~ (pq)FTTT(pq) ~ (pq)FTTF2. (pq) ~ rpTTTTFFFFqTTFFTTFF(pq)TTFFFFFFrTFTFTFTF(pq) ~ rTTFTFTFT~rFTFTFTFTDouble Negative Property ~ (~p) pp(~p)~ (~p)TFFTTFExample:It is not true that I am not happySolution:Khawaja Tariq Mahmood.Page 2Lecture # 2TRUTH TABLELet p = I am happythen ~ p = I am not happyand ~(~ p) = It is not true that I am not happySince ~ (~p) pHence the given statement is equivalent to: I am happyExample:Show by truth table that ~ (pq) and ~p ~q are not logically equivalentSolution:pTTFFqTFTF(pq)TFFF~ (pq)FTTT~pFFTT~qFTFT~p ~qFFFT~pFFTT~qFTFT~p ~qFTTTDE MORGANS LAWS:1)pq p/q / Symbolically ~ (p q) ~p ~q2)pq p/q / Symbolically: ~ (p q) ~p ~q//PROVE LOGICALLY ~ (p q) ~p ~qpTTFFqTFTFKhawaja Tariq Mahmood.(pq)TFFF~ (pq)FTTTPage 3Lecture # 2TRUTH TABLETAUTOLOGY:A tautology is a statement form that is always true regardless of the truth values of thestatement variables. A statement whose form is a

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