Encyclopedia > Laws of logic

  Article Content

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



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Bugatti

... Ettore Bugatti 2 Under Romano Artioli 3 Collectors 4 External links Under Ettore Bugatti Bugatti Royale Only a few models of each of Ettore Bugatti' ...

 
 
 
This page was created in 23.4 ms