relation

a relation is a set of ordered pairs.
[cite:;taken from @sets_enderton_1977 chapter 3 relations and functions]

a relation on a set $\text{[math]}$ is a subset $\text{[math]}$ of the cartesian product $\text{[math]}$ .
[cite:;taken from @topology_munkres_2014 chapter 1 set theory and logic]

some stuff from college

assuming $\text{[math]}$ and $\text{[math]}$ are sets, if $\text{[math]}$ then $\text{[math]}$ is a relation from $\text{[math]}$ to $\text{[math]}$ .