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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Logical negation

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