TeXipedia

neg

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 propositional logic to negate boolean expressions
  • Appears frequently in set theory for complement operations
  • Important in formal reasoning and mathematical proofs
  • Used in discrete mathematics and algorithm specifications
  • Often combined with other logical operators to form complex logical expressions

Examples

Logical negation in a propositional logic statement

p  ⟹  ¬qp \implies \neg q 
p \implies \neg q

Set complement notation in set theory

A∩¬A=∅A \cap \neg A = \emptyset 
A \cap \neg A = \emptyset

Truth table header showing negation of a proposition

p¬pTFFT\begin{array}{c|c} p & \neg p \\ \hline T & F \\ F & T \end{array} 
\begin{array}{c|c} p & \neg p \\ \hline T & F \\ F & T \end{array}