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De Morgan’s Laws

\neg(p \land q) \equiv \neg p \lor \neg q

The negation of an and statement is logically equivalent to the or statement in which each component is negated.

\neg(p \lor q) \equiv \neg p \land \neg q

The negation of an or statement is logically equivalent to the and statement in which each component is negated.

\displaystyle p

\displaystyle q

\displaystyle \neg p

\displaystyle \neg q

\displaystyle p \land q

\displaystyle \neg(p \land q)

\displaystyle \neg p \lor \neg q

T T F F T F F
T F F T F T T
F T T F F T T
F F T T F T T