A binary operator f on a set X is commutative if f(x, y) = f(y, x) for all x, y ϵ X. state...

A binary operator f on a set X is commutative if f(x, y) = f(y, x) for all x, y ϵ X. state whether the given function f is a binary operator on the set X. If f is not a binary operator, state why. State whether or not each binary operator is commutative.

  f(x, y)= x − y,  X = {1,2,...}