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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:

${\displaystyle {\text{Logical Negation}}\!}$

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

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:

${\displaystyle {\text{Variant Notations}}\!}$

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

Syllabus

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.

• Logical Negation, InterSciWiki
• Logical Negation, Wikinfo
• Logical Negation, Wikiversity
• Logical Negation, Wikiversity Beta
• Logical Negation, Wikipedia