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:

 $$p\!$$ $$\lnot p\!$$ $$\operatorname{F}$$ $$\operatorname{T}$$ $$\operatorname{T}$$ $$\operatorname{F}$$

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.