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 NOT p (also written as ~p or ¬p) is as follows:


Logical Negation
p ¬p
F T
T F


The logical negation of a proposition p is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:


Variant Notations
Notation Vocalization
\(\bar{p}\) bar p
\(p'\!\) p prime,

p complement

\(!p\!\) bang p


See also

Logical operators

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