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Discrete Structure lecture_2

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DISCREAT STRUCTURE LECTURE # 2 TRUTH TABLE KHAWAJA TARIQ MAHMOOD Lecture # 2 TRUTH TABLE CONSTRUCT TRUTH TABLE: 1. (pq)  ~ (pq) P T T F F (pq) T T T F q T F T F (pq) T F F F ~ (pq) F T T T (pq)  ~ (pq) F T T F 2. (pq)  ~ r p T T T T F F F F q T T F F T T F F (pq) T T F F F F F F r T F T F T F T F (pq)  ~ r T T F T F T F T ~r F T F T F T F T Double Negative Property ~ (~p)  p p (~p) ~ (~p) T F F T T F Example: “It is not true that I am not happy” Solution: Khawaja Tariq Mahmood. Page 2 Lecture # 2 TRUTH TABLE Let p = “I am happy” then ~ p = “I am not happy” and ~(~ p) = “It is not true that I am not happy” Since ~ (~p)  p Hence the given statement is equivalent to: “I am happy” Example: Show by truth table that ~ (pq) and ~p  ~q are not logically equivalent Solution: p T T F F q T F T F (pq) T F F F ~ (pq) F T T T ~p F F T T ~q F T F T ~p  ~q F F F T ~p F F T T ~q F T F T ~p  ~q F T T T DE MORGAN’S LAWS: 1) p q   p/ q / Symbolically ~ (p  q)  ~p  ~q 2) p q   p/ q / Symbolically: ~ (p  q)  ~p  ~q / / PROVE LOGICALLY ~ (p  q)  ~p  ~q p T T F F q T F T F Khawaja Tariq Mahmood. (pq) T F F F ~ (pq) F T T T Page 3 Lecture # 2 TRUTH TABLE TAUTOLOGY: A tautology is a statement form that is always true regardless of the truth values of the statement variables. A statement whose form is a ...
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