[[Naïve set theory MOC]]
# Relation

A **relation** between [[set|sets]] $A$ and $B$ is a construct which _relates_ elements $a \in A$ or $b\in B$, so that $a \sim b$ is either true or false. #m/def/set
We may therefore define a relation $R$ as the following [[subset]] of the [[cartesian product]] $A \times B$
$$
\begin{align*}
R = \left\{ (a, b) \in A \times B : a \sim b \right\}
\end{align*}
$$
or equivalently as a function $A \times B \to \Omega$.
A special class of relation is the [[Equivalence relation]].

See also [[Relation class]].

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