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