LogicalEquiv - q r ) ( p r ) ( q r ) ( p q ) r ( p q ) ( p...

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Logical Equivalences: 1. Table 6 on Page 24 Equivalence Name p T p Identity laws * p F p p T T Domination laws * p F F p p p Idempotent laws * p p p ¬ ( ¬ p ) p Double negation law * p q q p Commutative laws * p q q p ( p q ) r p ( q r ) Associative laws * ( p q ) r p ( q r ) p ( q r ) ( p q ) ( p r ) Distributive laws * p ( q r ) ( p q ) ( p r ) ¬ ( p q ) ( ¬ p ) ( ¬ q ) De Morgan’s laws * ¬ ( p q ) ( ¬ p ) ( ¬ q ) p ( p q ) p Absorption laws * p ( p q ) p p ( ¬ p ) T Negation laws * p ( ¬ p ) F 2. Table 7 on Page 25 Equivalences involving conditional statements p q ( ¬ p ) q * p q ( ¬ q ) ( ¬ p ) * p q ( ¬ p ) q p q ≡ ¬ [ p ( ¬ q )] ¬ ( p q ) p ( ¬ q ) ( p q ) ( p r ) p (
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Unformatted text preview: q r ) ( p r ) ( q r ) ( p q ) r ( p q ) ( p r ) p ( q r ) ( p r ) ( q r ) ( p q ) r 3. Table 8 on Page 25 Equivalences involving biconditional statements p q ( p q ) ( q p ) * p q ( p ) ( q ) * p q ( p q ) [( p ) ( q )] ( p q ) p ( q ) I expect you to know the (*) equivalences....
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This note was uploaded on 04/06/2010 for the course LAPS MATH 1190 taught by Professor Adachan during the Spring '10 term at York University.

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LogicalEquiv - q r ) ( p r ) ( q r ) ( p q ) r ( p q ) ( p...

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