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

Log in or registerto write something here or to contact authors.