Question: How many different relations are there from a set with m elements to a set with n elements?
Let R be a relation from a set A to a set B. The inverse relation from B to A, denoted by R-1, is the set of ordered pairs {(b, a) | (a, b) ∈ R}. The complementary relation R is the set of ordered pairs {(a, b) | (a, b) ∈ R}