---
tag: 0XR7A7RSXB
kind: definition
name: Negation
msc: [03B05]
defines: 029JBBF693
uses: [0ZGC7ZESYN]
sources:
  - url: https://en.wikipedia.org/wiki/Negation
    locator: lead section
---

## Definition

Let $p$ be a [[proposition|0ZGC7ZESYN]].
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|0NFAGWH84K]].

## 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.