maths pls help

[LoveToStack]

Let f: X → Y be a function. Let A' and A'' be subsets of X.
Which of the following statements about images and preimages is true (if any)? In each case give either a proof or a counterexample.

(1) f(A'\A'') = f(A') \ f(A'')

(2) A' ⊆ f ^-1(f(A'))

I've got some 'reasoning' for the first one to suggest it is true but I'm not confident in it at all. And for the second statement I'm struggling to see how they aren't simply equivalent (which is stronger than what the actual statement suggests).

Any help much appreciated.

[The Don]

@Kardan; is your best bet for help