Relation

set-theory

Definition

Relation

A relation $R$ is a set of ordered pairs that associates elements from set $A$, the domain, with elements of set $B$, the codomain, denoted as $R\subseteq A\times B$ (using the Cartesian Product).

An element $a\in A$ is related to an element $b\in B$ by the relation $R$ if $(a,b)\in R$, which can be denoted:

$$aRb:=(a,b)\subseteq R$$