question for discrete mathematics

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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?
 
Sorry for translate problem. I mean that "axiom of the choice ". And yes P means power set.
 
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Sorry for translate problem. I mean that "axiom of the choice ". And yes P means power set.
That is fine: for every family of sets there is a choice function.
But what are we to do with it? We know that it exists, but to what end?
That is the part of this post you fave failed to make clear.
 
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