Question

So I have a lot of different statements, that I need to prove. So maybe if I could get help on how to start. One of the statements are: \[H∩K=\emptyset =>f^{-1}(H)∩f^{-1}(K)=\emptyset \]

Answer 1

What happens when you take \[f^{-1}\]to a set?

Answer 2

I was thinking about the fact that:\[f^{-1}(H)=\left\{ x \in X|f(x) \in H \right\}\subseteq X\]

Answer 3

Do we know anything else about f?