Table of Logical Equivalences

Table of Logical Equivalences

Commutative

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

Idempotent

p p p

p p p

Universal Bound

p T T

p F F

De Morgan's

(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)

Rules of Inference

Modus Ponens p = q

Modus Tollens

p = q

p

q

q

p

Elimination p q

Transitivity

p = q

q

q = r

p

p = r

Generalization p = p q Specialization

p q = p

q = p q

p q = q

Conjunction p

Contradiction Rule p = F

q

p

pq

? 2011 B.E.Shapiro for integral-. This work is licensed under a Creative Commons Attribution-NonCommercial-

ShareAlike 3.0 Unported License. Revised July 20, 2011.

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