Question

Let A, B \(\in \mathbb R\) prove or disprove
\(f^{-1}(A\B)=f^{-1}(A)\f^{-1}(B)\), \(f:\mathbb R\rightarrow \mathbb R\)
Please, help

Answer 1

im thinking we can disprove it ....

Answer 2

let \(x \in f^{-1}(A\B)\) , then there exists \(f(x) \in (A\B\) )
f(x) in A --> f^- (x) in f^-(A)
f(x) is not in B --> f^-(x) is not in f^-(B)
hence, f^-(x) in f^-(A)\f^-(B)
is it valid?

Answer 3

I got it