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Laws of Logic

The following laws of logic are valid in propositional logic and can be proved with truth tables. They are also valid in any boolean algebra. See logical operator for the meaning of the symbols.

Summary of the Laws of Logic

Idempotent p ∨ p ≡ p
p ∧ p ≡ p
Associative (p ∧ q ) ∧ r ≡ p ∧ ( q ∧ r )
(p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r )
Commutative p ∧ q ≡ q ∧ p
p ∨ q ≡ q ∨ p
Distributive p ∨ ( q ∧ r ) ≡ ( p ∨ q ) ∧ ( p ∨ r )
p ∧ ( q ∨ r ) ≡ ( p ∧ q ) ∨ ( p ∧ r )
Identity p ∧ T ≡ p
p ∨ F ≡ p
Annihilation p ∨ T ≡ T
p ∧ F ≡ F
Complement p ∨ ¬ p ≡ T
p ∧ ¬ p ≡ F
¬ T ≡ F
¬ F ≡ T
Involution ¬ ¬ p ≡ p
DeMorgan's p ∨ q ≡ ¬ ( ¬ p ∧ ¬ q )
p ∧ q ≡ ¬ ( ¬ p ∨ ¬ q )
Absorption p ∧ ( p ∨ q ) ≡ p
p ∨ ( p ∧ q ) ≡ p

Referenced By

Boolean operator | Logical operator

 

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Laws of Logic".

 

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