Binary Relations

Binary relation

Take two arbitrary sets, $A$ and $B$. Remember that the Cartesian product $A\times B$ is a set containing ordered pairs $(a,b)$ so that $a\in A$ and $b\in B$. Any subset $R$ of $A\times B$ is a relation from $A$ to $B$. We call this a binary relation because it’s defined for two sets. We’ll simply use the term “relation” for binary relations unless mentioned otherwise.

Examples

Let $A=\{1,2,3,4\}$ and $B=\{a,b,c\}$.