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FinalCheatSheet - Name Equivalence Identity laws pTp pFp...

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Name: 6 Equivalence Equivalence Identity laws Domination laws p T p p T T p F p p F F Idempotent laws Double negation law p p p ¬ ( ¬ p ) p p p p Commutative laws Associative laws p q q p ( p q ) r p ( q r ) p q q p ( p q ) r p ( q r ) Distributive laws De Morgan’s laws p ( q r ) ( p q ) ( p r ) ¬ ( p q ) ( ¬ p ) ( ¬ q ) p ( q r ) ( p q ) ( p r ) ¬ ( p q ) ( ¬ p ) ( ¬ q ) Absorption laws Negation laws p ( p q ) p p ( ¬ p ) T p ( p q ) p p ( ¬ p ) F p q ( ¬ p ) q (1) p q ( p q ) ( q p ) (3) p q ( ¬ q ) ( ¬ p ) (2) p q ( ¬ p ) ( ¬ q ) (4) Rule of Inference Rule of Inference Rule of Inference Modus ponens Modus tollens Hypothetical syllogism p p q q p q ¬ q ¬ p p q q r p r Disjunctive syllogism Addition Simplication p q ¬ p q p p q p q p Conjunction Resolution p q p q p q ¬ p r q r Rule of Inference Rule of Inference Universal instantiation Universal generalization xP ( x ) P ( c ) P ( c ) for an arbitrary c xP ( x ) Existential instantiation Existential generalization xP ( x ) P ( c ) for some element

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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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FinalCheatSheet - Name Equivalence Identity laws pTp pFp...

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