Originally Posted by

**osudude** Here is the problem:

show that if f:A $\displaystyle \rightarrow $ B and G, H are substes of B, then

$\displaystyle f^{-1}$(G$\displaystyle \cup$H) = $\displaystyle f^{-1}$ (G)$\displaystyle \cup$ $\displaystyle f^{-1}$(H)

and

$\displaystyle f^{-1}$(G$\displaystyle \cap$H) = $\displaystyle f^{-1}$ (G)$\displaystyle \cap$ $\displaystyle f^{-1}$(H)

So I understand the main principle behind an inverse, such that if f(x)$\displaystyle \in$H, then x$\displaystyle \in f^{-1}$(H). I also understand the proof for inverse composite functions. But this is confusing. How do I prove this?? Thank you