Question

5. Suppose F is a nonempty family of sets. Let I = ∪F and J = ∩F. Suppose also that J ≠ Ø , and notice that it follows that for every X ∈ F, X ≠ Ø , and also that I ≠ Ø. Finally, suppose that {A i | i ∈ I } is an indexed family of sets.

(a) Prove that ∪ i∈I A i = ∪ X ∈F (∪ i∈X A i ).

Answer 1

Hmm I wouldn't know how to approach this one.
Lemme rewrite part a) though so it's a little easier to read.

Answer 2

Prove that\[\large\rm \bigcup_{i\in I}A_i\quad=\quad \bigcup_{X\in F}\left(\bigcup_{i\in X}A_i\right)\]

Answer 3

Hola

Answer 4

hint:
we can write this statement:
\[\Large i \in I \Rightarrow \quad \exists X \in I|i \in X\quad and\quad X \in F\]

Answer 5

I would like to see the snapshot of the problem.

Answer 6

http://pasteboard.co/1LEIHUYi.png