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 $p\!$ Document history

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