The negation of some [[Proposition]] $P$ is a [[Logical Operator]] that is denoted by $\neg P$ or $\sim P$.
The [[Logical Negation]] is the [[Proposition]]:
>[!quote] It is *not* the case that $P$.
It can be read as "**not** $P
quot;.
The negation is also [[Logical Inverse|Invertible]], with the operation being its own [[Logical Inverse]]:
$\huge \neg\pa{ \neg P} = P $
$ \huge \begin{align}
\let n &\in \Z \\
(\neg)^{2n}(P) &= P\\
(\neg)^{2n+1}(P) &= \neg P
\end{align}
$
#### Truth Table
| $P$ | $\neg P$ |
| ----- | -------- |
| *T* | **F** |
| **F** | *T* |