In

boolean algebra, the propositions p and q are called logically equivalent if p <-> q (

biconditional) is a

tautology. The notation p <==> q denotes that p and q are logically equivalent (modified slightly to fit into

ASCII).

See Everything Logic Symbols for the meanings of the other symbols.

Identity laws: p * T <==> p
p ^ F <==> p
Domination laws: p * T <==> T
p ^ F <==> F
Idempotent laws: p ^ p <==> p
p * p <==> p
Double negation law: ~( ~p ) <==> p
Commutative laws: p ^ q <==> q ^ p
p * q <==> q * p
Associative laws: ( p ^ q ) ^ r <==> p ^ ( q ^ r )
( p * q ) * r <==> p * ( q * r )
Distributive laws: p ^ ( q * r ) <==> ( p ^ q ) * ( p ^ r )
p * ( q ^ r ) <==> ( p * q ) ^ ( p * r )
De Morgan's laws: ~( p * q ) <==> ~p ^ ~q
~( p ^ q ) <==> ~p * ~q