eolas/Logic/DeMorgan's_Laws.md

tags
Logic propositional-logic derivation-rules theorems-axioms-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.

\sim (P & Q) \equiv \sim P \lor \sim Q

The equivalence is demonstrated with the following truth-table

Second Law

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

\sim (P \lor Q) \equiv \sim P & \sim Q