Philosophy Index

De Morgan’s laws

De Morgan's laws are rules in logic which state that "not (P or Q)" is equivalent to "(not P) and (not Q)", while "not (P and Q)" is equivalent to "(not P) or (not Q)".

These laws may be expressed formally as follows:

¬(α ∧ β) ≡ ¬α ∨ ¬β


¬(α ∨ β) ≡ ¬α ∧ ¬β

Note: De Morgan’s laws for symbolic logic should not be confused with the similar De Morgan’s laws for set identities.