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
Johann Karl Friedrich Rosenkranz

... on the one hand, and the "extreme left" represented by Strauss, Feuerbach and Bruno Bauer. Of his numerous writings, the following may be mentioned: ...

 
 
 
This page was created in 22.6 ms