## cinar Group Title I need some help.. proof indexed family of set distributive law.. one year ago one year ago

1. cinar Group Title

2. satellite73 Group Title

hard to write because saying it says the same thing. but i think the way to do it is to show that each is contained in the other pick some element on the left, say $$x$$ and show that it is in the right an vice versa if it is in the left, then either $$x\in B$$ or $$x\in \cap A_{\alpha\in I}$$ meaning $$\exists\beta\in I$$ such that $$x\in A_\beta$$

3. satellite73 Group Title

then if $$x\in B$$ it must be in $$A_{\alpha}\cup B$$ for any $$\alpha$$ and if $$a\notin B$$ then by the proceeding it must be in some $$A_{\beta}$$ oh crap i got my modifier wrong!!

4. satellite73 Group Title

if $$x\in \cap A_{\alpha \in I}$$ it is in ALL $$A_{\alpha}$$

5. satellite73 Group Title

so $$\forall \alpha \in I$$ we know $$x\in A_{\alpha}$$ and therefore $$x\in \cap (A_{\alpha \in I}\cup B)$$