De Morgan's Rules

boolean-algebra

Definition

De Morgan's Rules

In propositional logic, De Morgan’s rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation:

• $A\wedge B⟺\neg A\vee \neg B$
• $A\vee B⟺\neg A\wedge \neg B$

Naturally, this can be applies to quantifiers:

• $\forall x:P(x)⟺\nexists x:\neg P(x)$
• $\exists x:P(x)⟺/\forall x:\neg P(x)$