# Logical negation

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 NOT p (also written as ~p or ¬p) is as follows:

Logical Negation
p ¬p
F T
T F

The logical negation of a proposition p is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:

Variant Notations
Notation Vocalization
$$\bar{p}$$ bar p
$$p'\!$$ p prime,

p complement

$$!p\!$$ bang p