# Logical equality

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☞ This page belongs to resource collections on Logic and Inquiry.

**Logical equality** is an operation on two logical values, typically the values of two propositions, that produces a value of *true* if and only if both operands are false or both operands are true.

The truth table of \(p ~\operatorname{EQ}~ q,\) also written \(p = q,\!\) \(p \Leftrightarrow q,\!\) or \(p \equiv q,\!\) appears below:

\(p\!\) | \(q\!\) | \(p = q\!\) |

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

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

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

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

## Syllabus

### Focal nodes

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

- Logical Equality @ P2P Foundation
- Logical Equality @ Subject Wikis
- Logical Equality @ Wikiversity Beta

### 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.