# 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.

The truth table of ${\displaystyle \operatorname {NOT} ~p,}$ also written ${\displaystyle \lnot p,\!}$ appears below:

 ${\displaystyle p\!}$ ${\displaystyle \lnot p\!}$ ${\displaystyle \operatorname {F} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {T} }$ ${\displaystyle \operatorname {F} }$

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

 ${\displaystyle {\text{Notation}}\!}$ ${\displaystyle {\text{Vocalization}}\!}$ ${\displaystyle {\bar {p}}\!}$ ${\displaystyle p\!}$ bar ${\displaystyle {\tilde {p}}\!}$ ${\displaystyle p\!}$ tilde ${\displaystyle p'\!}$ ${\displaystyle p\!}$ prime ${\displaystyle p\!}$ complement ${\displaystyle !p\!}$ bang ${\displaystyle p\!}$

## 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.