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 $$p$$.

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 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
Different symbols that you may encounter that mean the same thing as $$\neg p$$ are: