Logical negation

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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 $\operatorname{NOT}~ p,$ also written $\lnot p,\!$ appears below:

$\text{Logical Negation}\!$

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

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:

$\text{Variant Notations}\!$

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

Syllabus

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Logical operators

Exclusive disjunction Logical conjunction Logical disjunction Logical equality

Logical implication Logical NAND Logical NNOR Negation

Related topics

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Relation theory Relative term Sign relation Triadic relation

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Inquiry Dynamics of inquiry

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Descriptive science Normative science

Pragmatic maxim Truth theory

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Document history

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