(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose F is a nonempty family of sets and B is a set. Prove that B U (∩F) = ∩_{AЄF}(B U A).

2. Relevant equations

3. The attempt at a solution

Let x Є (B U (∩F)). This means (x Є B) ν (x Є ∩F). x Є F = {x l [itex]\forall[/itex]AЄF(xЄA)}.

Assume AЄF, then xЄA. Therefore, xЄB ν xЄA. This is equivalent to ∩_{AЄF}(BUA).

Let xЄ ∩_{AЄF}(BUA). This means xЄ{x l[itex]\forall[/itex]A(AЄF[itex]\rightarrow[/itex]xЄ(BUA)}. Assume AЄF, then xЄ(BUA). Thus, this is equivalent to BU(∩F).

Therefore, BU(∩F) = ∩_{AЄF}(BUA).

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# Did I assume too much in this proof?

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