Let f : X → Y and ∼ be as in the previous problem. For y ∈ f(X), define F(y) = f ^-1 ({y}) (where f ^-1 (A) = {x ∈X : f(y) ∈ A}). Show that F is a bijection between f(X) and the set of equivalence classes in X under the relation ∼.

*Previous problem states "For a, b ∈ X, declare a ∼ b if f(a) = f(b)."