De Morgan's Laws (Logic)/Conjunction

Theorem

Formulation 1

$p \land q \dashv \vdash \neg \paren {\neg p \lor \neg q}$

Formulation 2

$\vdash \paren {p \land q} \iff \paren {\neg \paren {\neg p \lor \neg q} }$

As a definition

$p \land q := \neg \left({\neg p \lor \neg q}\right)$

Also see

• De Morgan's Laws (Set Theory) for a set theoretic application.
• De Morgan's Laws (Predicate Logic) for a predicate logic application.