Relations (Sets)

Definition #

A relation R from the elements of set A to the elements of set B is a subset of A×B.

…alternatively…

Let A and B be two non-empty sets, then every subset of A×B defines a relation from A to B and ever relation from A to B is a subset of A×B.

Let R⊆A×B and (a,b)∈R. Then we say that a is related to b by the relation R and write it as aRb. If (a,b)∈R, we write it as aRb