---
type: "concept"
title: "Relation (set theory)"
slug: "relation-set-theory"
language: "en"
translationGroupId: "cmr1xcysw0005mo010hmsy43s"
domain: "Logic"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

In [[Set theory|set theory]], a relation $R$ between two sets $A$ and $B$ is a [[Subset|subset]] of the [[Cartesian product|cartesian product]] $A\times B$.
For $a\in A$ and $b\in B$, one says that $a$ is related to $b$, denoted as $a \;R \;b$, when $(a,b)\in R$.

##### Remarks and examples
- When $A=B$, one speaks of a relation on $A$.
- A [[function|function]] is itself a special kind of relation.