# Exclusive disjunction

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**Exclusive disjunction**, also known as **logical inequality** or **symmetric difference**, is an operation on two logical values, typically the values of two propositions, that produces a value of *true* just in case exactly one of its operands is true.

The truth table of \(p ~\operatorname{XOR}~ q,\) also written \(p + q~\!\) or \(p \ne q,\!\) appears below:

\(p\!\) | \(q\!\) | \(p ~\operatorname{XOR}~ q\) |

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

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

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

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

The following equivalents may then be deduced:

\(\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\[6pt] & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\[6pt] & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\) |

## Syllabus

### Focal nodes

### Peer nodes

- Exclusive Disjunction @ InterSciWiki
- Exclusive Disjunction @ MyWikiBiz
- Exclusive Disjunction @ Subject Wikis
- Exclusive Disjunction @ Wikiversity
- Exclusive Disjunction @ Wikiversity Beta

### Logical operators

Template:Col-breakTemplate:Col-breakTemplate:Col-end### Related topics

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

### Relational concepts

### Information, Inquiry

### Related articles

- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems

- Prospects for Inquiry Driven Systems
- Introduction to Inquiry Driven Systems
- Inquiry Driven Systems : Inquiry Into Inquiry

## 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.

- Exclusive Disjunction, InterSciWiki
- Exclusive Disjunction, MyWikiBiz
- Exclusive Disjunction, Subject Wikis
- Exclusive Disjunction, Wikinfo
- Exclusive Disjunction, Wikiversity
- Exclusive Disjunction, Wikiversity Beta
- Exclusive Disjunction, Wikipedia