# Logical negation

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**Logical negation** is an operation on one logical value, typically the value of a proposition, that produces a value of *true* when its operand is false and a value of *false* when its operand is true.

The truth table of \(\operatorname{NOT}~ p,\) also written \(\lnot p,\!\) appears below:

\(p\!\) | \(\lnot p\!\) |

\(\operatorname{F}\) | \(\operatorname{T}\) |

\(\operatorname{T}\) | \(\operatorname{F}\) |

The negation of a proposition \(p\!\) may be found notated in various ways in various contexts of application, often merely for typographical convenience. Among these variants are the following:

\(\text{Notation}\!\) | \(\text{Vocalization}\!\) |

\(\bar{p}\!\) | \(p\!\) bar |

\(\tilde{p}\!\) | \(p\!\) tilde |

\(p'\!\) | \(p\!\) prime \(p\!\) complement |

\(!p\!\) | bang \(p\!\) |

## Syllabus

### Focal nodes

Template:Col-breakTemplate:Col-breakTemplate:Col-end### Peer nodes

### Logical operators

### Related topics

- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic

### Relational concepts

### Information, Inquiry

### Related articles

## Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

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