# Math Help - Need help with a subset proof

1. ## Need help with a subset proof

Here's the problem:

Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y.
Prove that f(f-1(A)) is a subset of A.

Any help is much appreciated!

2. ## Re: Need help with a subset proof

Originally Posted by widenerl194
Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y.
Prove that f(f-1(A)) is a subset of A.
Can you describe what $f(f^{-1}(A))$ looks like in set-theoretic terms?
If not, there is a place for you to begin,

3. ## Re: Need help with a subset proof

I think it might be

f(f^-1(A)) = f(x) is an element of X such that f(x) is an element of f(A).