Formula Sheet

Formula Sheet - Math 326 - Formula Sheet California State...

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Unformatted text preview: Math 326 - Formula Sheet California State University, Northridge Table of Logical Equivalences p ∧ q ⇐⇒ q ∧ p p ∨ q ⇐⇒ q ∨ p Associative (p ∧ q ) ∧ r ⇐⇒ p ∧ (q ∧ r) (p ∨ q ) ∨ r ⇐⇒ p ∨ (q ∨ r) Distributive p ∧ (q ∨ r) ⇐⇒ (p ∧ q ) ∨ (p ∧ r) p ∨ (q ∧ r) ⇐⇒ (p ∨ q ) ∧ (p ∨ r) Identity p ∧ T ⇐⇒ p p ∨ F ⇐⇒ p Negation p∨ ∼ p ⇐⇒ T p∧ ∼ p ⇐⇒ F Double Negative ∼ (∼ p) ⇐⇒ p Commutative Idempotent p ∧ p ⇐⇒ p p ∨ p ⇐⇒ p Universal Bound p ∨ T ⇐⇒ T p ∧ F ⇐⇒ F ∼ (p ∧ q ) ⇐⇒ (∼ p) ∨ (∼ q ) ∼ (p ∨ q ) ⇐⇒ (∼ p) ∧ (∼ q ) Absorption p ∨ (p ∧ q ) ⇐⇒ p p ∧ (p ∨ q ) ⇐⇒ p Conditional (p =⇒ q ) ⇐⇒ (∼ p ∨ q ) ∼ (p =⇒ q ) ⇐⇒ (p∧ ∼ q ) De Morgan’s Rules of Inference Modus Ponens p =⇒ q Modus Tollens p =⇒ q p ∴q Elimination ∼q ∴∼ p p∨q Transitivity p =⇒ q ∼q ∴p Generalization q =⇒ r ∴ p =⇒ r p =⇒ p ∨ q Specialization q =⇒ p ∨ q Conjunction p q ∴p∧q p ∧ q =⇒ p p ∧ q =⇒ q Contradiction Rule ∼ p =⇒ F ∴p ...
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This note was uploaded on 06/12/2011 for the course MATH 103 taught by Professor Wouters during the Spring '08 term at Wisc Oshkosh.

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