This site is supported by donations to The OEIS Foundation.

# Logical negation

Logical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true.

A truth table for $\mathrm {NOT} ~p,$ also written $\lnot p,$ appears below:

 $p$ $\lnot p$ $\mathrm {F}$ $\mathrm {T}$ $\mathrm {T}$ $\mathrm {F}$ The negation of a proposition $p$ may be found notated in various ways in various contexts of application, often merely for typographical convenience.  Among these variants are the following:

 ${\text{Notation}}$ ${\text{Vocalization}}$ ${\bar {p}}$ $p$ bar ${\tilde {p}}$ $p$ tilde $p'$ $p$ prime $p$ complement $!p$ bang $p$ A logical graph for $\lnot p$ is shown below:

The traversal string of this graph is ${\texttt {(}}p{\texttt {)}}.$ The proposition $\lnot p$ may be taken as a Boolean function $f(p)$ having the abstract type $f:\mathbb {B} \to \mathbb {B} ,$ where $\mathbb {B} =\{0,1\}$ is interpreted in such a way that $0$ means $\mathrm {false}$ and $1$ means $\mathrm {true} .$ A Venn diagram for $\lnot p$ indicates the region where $\lnot p$ is true by means of a distinctive color or shading.  In this case the region is a single cell, as shown below:

## Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.