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De Morgan's Laws

These laws relate the complement of a conjunction to the disjunction of complements, and vice versa: \neg(A \land B) = \neg A \lor \neg B \text{ and } \neg(A \lor B) = \neg A \land \neg B.

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The statement of the theorem

For any Boolean variables

A

and

B

, the following identities hold: \n1. Complement of Conjunction:

\neg(A \land B) = \neg A \lor \neg B

.\n2. Complement of Disjunction:

\neg(A \lor B) = \neg A \land \neg B

Source: Wikipedia