Application

[MafaldaRSF]

It’s in french but basically I just have to show that the left part equals the right one. I’ve tried to prove it by showing the positive but I don’t achieve a valid/logical result. Can anyone help?

 

[blamocur]

I would prove this by contradiction: assume that [imath]f(A)\cup B \neq \empty[/imath] then show that [imath]A \cup f^{-1}(B)[/imath] is non-empty too. Then vice versa.