Let X and Y be sets and f:X->Y be a function. For A is a proper subset of X and B is a proper subset of Y, recall the definitions of f(A) is a proper subset of Y and f^-1(B) is a proper subset of X,
f(A)={f(a):a is an element of A} and f^-1(B)={x is an element of X:f(x) is an element of B}
Prove:
A is a proper subset of f^-1(f(A)) and f(f^-1(B)) is a proper subset of B; equality need not hold in either case.
Not even sure where to begin. Help, please!