Logical negation

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This page belongs to resource collections on Logic and Inquiry.

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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Focal nodes

Peer nodes

Logical operators

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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.