Binary relation

For sets $A$ and $B$, a (binary) relation from $A$ to $B$ is any subset $R$ of the [[Cartesian product of sets|Cartesian product]] $A \times B$ or otherwise a set consisting of some ordered pairs.

We use notation $\boxed{aRb}$ to denote that $(a,b)\in R$, and say that $a$ is $R$-related to $b$. If $(a,b)\notin R$, then we right $\boxed{a\cancel{R}b}$.