Definition:Logical Not

Definition
The logical not or negation operator is a unary connective whose action is to reverse the truth value of the statement on which it operates.


 * $\neg \, p$ is defined as: $p$ is not true, or It is not the case that $p$ is true.

Thus the statement $\neg \, p$ is called the negation of $p$.

$\neg \, p$ is voiced not $p$.

In the statement $\neg \, p$, the scope of $\neg$ is $p$.

Boolean Interpretation
From the above, we see that the boolean interpretations for $\mathbf A$ under the model $\mathcal M$ are:


 * $\left({\neg \, \mathbf A}\right)_{\mathcal M} = \begin{cases}

T & : \mathbf A_{\mathcal M} = F \\ F & : \mathbf A_{\mathcal M} = T \end{cases}$

Truth Function
The logical not connective defines the truth function $f^\neg$ as follows:

Truth Table
The truth table of $\neg \, p$ is as follows:


 * $\begin{array}{|c||c|} \hline

p & \neg \, p \\ \hline F & T \\ T & F \\ \hline \end{array}$

Notational Variants
Various symbols are encountered that denote the concept of the logical not: