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 $p\!$

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