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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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.