Let f: A -> B and X be subsets of A.

Prove: X is a subset of f inverse of f(X)

Let b be in f(X) which implies b=f(a) where a is in X

f inverse of b=f inverse of f(a)=a which implies f inverse of b is in X

which implies X is a subset of f inverse of f(X)

qed

Did I do this correctly?

Thanks!