1. The problem statement, all variables and given/known data Prove or disprove that for any non empty sets X and Y, any subset A of X, and f:X->Y, f(f^-1(A))=A 2. Relevant equations 3. The attempt at a solution I know that for x element of A f(x) = f(A) so x is an element of f^-1(f(A)). If I can assume f is injective then I can go from here but that's not given in the problem..... Note that A is a subset of X not Y.