Originally Posted by

**issacnewton** hi

I have few doubts about one set theorem which I proved.

Suppose that $\displaystyle f:X\rightarrow Y$ with $\displaystyle A\subseteq X$

and $\displaystyle B\subseteq Y$ . I had to prove that

$\displaystyle A\subseteq f^{-1}(f(A))$

I did prove that but I have some questions. Shouldn't there be an equality

$\displaystyle A= f^{-1}(f(A))$ because when we talk about the inverse functions, we talk about one-to-one functions. So I can't think of situation

where

$\displaystyle \textstyle A\subset f^{-1}(f(A))$

Can you ? and question related to latex typesetting. how do I reduce font size ?

thanks