DeMorgan's Laws

DeMorgan's laws express some fundamental equivalences that obtain between the Boolean connectives.

First Law

The negation of a conjunction is logically equivalent to the disjunction of the negations of the original conjuncts.

\lnot (P \land Q) \leftrightarrow \lnot P \lor \lnot Q

The equivalence is demonstrated with the following truth-table

`P`	`Q`	`\lnot (P \land Q)`	`\lnot P \lor \lnot Q`
T	T	F	F
T	F	T	T
F	T	T	T
F	F	T	T ### Truth conditions

The negation of a disjunction is equivalent to the conjunction of the negation of the original disjuncts.

\lnot (P \lor Q) \leftrightarrow \lnot P \land \lnot Q

`P`	`Q`	`\lnot (P \lor Q)`	`\lnot P \land \lnot Q`
T	T	F	F
T	F	F	F
F	T	F	F
F	F	T	T