TeXipedia

lnot

Represents logical negation in mathematical logic and set theory, indicating the opposite or contradiction of a statement.

Overview

Essential for expressing logical operations and constructing formal proofs in mathematics and computer science.

  • Commonly used in truth tables and Boolean algebra
  • Appears frequently in discrete mathematics and formal logic
  • Important in set theory for expressing complementary sets
  • Often combined with other logical operators to form complex logical expressions
  • Particularly useful in writing mathematical proofs and expressing logical implications

Examples

Basic logical negation of a proposition P.

¬P    Q\lnot P \implies Q
\lnot P \implies Q

Negation in a compound logical statement.

(P¬Q)R(P \land \lnot Q) \lor R
(P \land \lnot Q) \lor R

De Morgan's law showing negation of conjunction.

¬(PQ)    ¬P¬Q\lnot(P \land Q) \iff \lnot P \lor \lnot Q
\lnot(P \land Q) \iff \lnot P \lor \lnot Q