Relation

A relation between 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 $𝐴 \times 𝐵$

𝑅 = {(𝑎, 𝑏) \in 𝐴 \times 𝐵 : 𝑎 \sim 𝑏}

or equivalently as a function $𝐴 \times 𝐵 \to Ω$ . A special class of relation is the Equivalence relation.