If |A| = k and |B| = m, how many relations are there between A and B? If in addition, |C| = n, how many ternary relations are there in A X B X C?
[Hint: recall the definition of a relation, and use of cardinality.]
In general there are $\displaystyle 2^{\left| X \right|\left| Y \right|}$ relations between X & Y.
(Be careful. That number includes the empty relation some texts/instructors object.)