De Morgan's Laws (Logic)/Disjunction of Negations

Theorems

Formulation 1

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

Formulation 2

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

Also see

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

Sources

• 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.2$: Some Remarks on the Use of the Connectives and, or, implies: Exercise $4$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): De Morgan's Laws
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): De Morgan's Laws