More formally, a binary relation is defined as an ordered triple: . is the domain of the relation, is the codomain, and is the subset of , also known as the relation’s graph.
Since by definition is a set of ordered pairs , then for all ordered pairs where and , one, and only one of the following must be true:
- ; this is read “a is R-related to b” and is written .
- ; this is read “a is not R-related to b” and is written .
Some properties of binary relations: