Here is what you have posted.
For every \(n\in\mathbb{N}\) if \(A_n=(n,n+1)\cap Q\),
if gives to \(A=\left\{A_n\right\}_{n\in\mathbb{N}}\) family
you have to write and explain selection function
for \(B=A\cup\left[P(N)\setminus\{\emptyset\}\right]\)
Speaking only for myself, I have not a clue what that means.
I say that having taught set theory & discrete mathematics for a long time.
I think that you need to clean up the English rendering.
More importantly you need to define the terms and explain exactly what is being asked for.
By \(P(N)\) do you mean powerset of \(\mathbb{N}~?\)
By selection function do you mean choice function?
If so what is your understanding of such a function?