What you are thinking of is an operation.

A relation is something like =,<=,>=,...

For example, on the set {1,2,3} you can define = as {(1,1),(2,2),(3,3)], i.e., the set of ordered pairs for which the relation holds.

Also,

> : {(2,1),(3,1),(3,2)}

< : {(1,2),(1,3),(2,3)}