2-2 Logic of Compound Statement III_수정.ppt - Logic of Compound Statement III Prof Anand Paul Tautology and Contradiction • A tautology is a

# 2-2 Logic of Compound Statement III_수정.ppt - Logic of...

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Logic of Compound Statement III Prof. Anand Paul Subscribe to view the full document.

A tautology is a statement that is always true p ¬p will always be true (Negation Law) A contradiction is a statement that is always false p ¬p will always be false (Negation Law) p p ¬ p p ¬ p T T F F T F Tautology and Contradiction A logical equivalence means that the two sides always have the same truth values Symbol is ≡ or We’ll use ≡, so as not to confuse it with the bi-conditional Logical Equivalence Subscribe to view the full document.

p T ≡ p Identity law p F ≡ F Domination law p T p T T T T F T F p F p F T F F F F F Logical Equivalences of And p p ≡ p Idempotent law p q ≡ q p Commutative law p p p p T T T F F F p q p q q p T T T T T F F F F T F F F F F F Logical Equivalences of And Subscribe to view the full document.

(p q) r ≡ p (q r) Associative law p q r p q (p q) r q r p (q r) T T T T T T T T T F T F F F T F T F F F F T F F F F F F F T T F F T F F T F F F F F F F T F F F F F F F F F F F Logical Equivalences of And p T ≡ T Identity law p F ≡ p Domination law p p ≡ p Idempotent law p q ≡ q p Commutative law (p q) r ≡ p (q r) Associative law Logical Equivalences of Or Subscribe to view the full document.

(p q) r ≡ p q r (p q) r ≡ p q r Similar to (3+4)+5 = 3+4+5 Only works if ALL the operators are the same!  • Winter '16
• Yoo Ki Young

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