Question: Let $$f:X\rightarrow Y.$$ If $$A\subset X, B\subset\ X,$$ prove that $$f(A)-f(B)\subset f(A) - f(B).$$
My Proof. (Please check if this is correct. THANK YOU!)
Let
$$ b\in f(A)-f(B).$$
This means that
$$b\in f(A),$$
hence there is an $a$ such that $$a\in A,$$
and similarly since
$$b\not\in f(B),$$
then (is this conclusion correct?)$$a \not\in B.$$
Therefore we can say that
$$a\in A-B,$$
hence
$$b\in f(A-B),$$
hence
$$f(A)-f(B)\subset f(A-B).$$