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Logical negation
☞ 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:
\(p\!\)  \(\lnot p\!\) 
\(\operatorname{F}\)  \(\operatorname{T}\) 
\(\operatorname{T}\)  \(\operatorname{F}\) 
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:
\(\text{Notation}\!\)  \(\text{Vocalization}\!\) 
\(\bar{p}\!\)  \(p\!\) bar 
\(\tilde{p}\!\)  \(p\!\) tilde 
\(p'\!\)  \(p\!\) prime \(p\!\) complement 
\(!p\!\)  bang \(p\!\) 
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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.