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Unformatted text preview: Logical Equivalences* Identity laws: Domination laws: Idempotent laws: Negation laws: Absorption laws: Double negation law: Commutative laws: Associative laws: Distributive laws: De Morgan's laws: Implication law: Biconditional law: More De Morgan's laws: p p p p p p p p T F T F p p T F p p p p p T p F p (p q) p p (p q) p
(p) p p q p q (p q) (p q) p p (p (p q q r r p p p (q r) p (q r)
(p q) (p r) (p q) (p r) q q (q (q q) q) r) r) p p p q p q p q (p q) (q p)
x P(x) x P(x) x P(x) x P(x) * from Rosen, p. 24 Rules of inference* Modus ponens: p p q q
q p q p Modus tollens: Hypothetical syllogism: p q q r p r p q p q p p q p q p p q p q p q p r q r
x P(x) P(c) P(c) for an arbitrary c x P(x) x P(x) P(c) for some unused c P(c) x P(x) Disjunctive syllogism: Addition: Simplification: Conjunction: Resolution: Universal instantiation: Universal generalization: Existential instantiation: Existential generalization: * from Rosen, pp. 66, 70 ...
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This note was uploaded on 01/18/2012 for the course CSCI 2610 taught by Professor Smith during the Fall '08 term at University of Georgia Athens.
- Fall '08
- Computer Science