Negation

Definition

Let $p$ be a proposition. The negation of $p$ is the proposition $\neg p$, read "not $p$". The proposition $\neg p$ is true when $p$ is false, and $\neg p$ is false when $p$ is true.

$p$	$\neg p$
T	F
F	T

Remarks

Other notations for $\neg p$ are $\sim p$ and $\overline{p}$. In classical logic, $\neg \neg p$ has the same truth value as $p$. This is the double negation law.

Explanations

L1 human

To negate a sentence, say that it is not the case. The negation of "$5$ is prime" is "$5$ is not prime". The first sentence is true, so its negation is false.