Equivalency Laws That You Must Know By Heart

p∨¬p⇔TTautology Law
¬(¬p)⇔pDouble Negation Law
p∨F⇔p
p∧T⇔p
Identity Laws
p∨q⇔q∨p
p∧q⇔q∧p
Commutative Laws
(p∨q)∨r⇔p∨(q∨r)
(p∧q)∧r⇔p∧(q∧r)
Associative Laws
¬(p∨q)⇔¬p∧¬q
¬(p∧q)⇔¬p∨¬q
DeMorgan's Laws
p→q⇔¬p∨qImplication Law
p→q⇔¬q→¬pContrapositive Law
¬(p→q)⇔p∧¬qNegation of Implication Law
p∨(q∧r)⇔(p∨q)∧(p∨r)
p∧(q∨r)⇔(p∧q)∨(p∧r)
Distributive Laws
p∧¬p⇔FContradiction Law
p∨T⇔T
p∧F⇔F
Domination Laws
p∨p⇔p
p∧p⇔p
Idempotent Laws
p∨(p∧q)⇔p
p∧(p∨q)⇔p
Absorption Laws
[(p→q)∧(q→p)]⇔p↔qBiconditional Equivalency