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## Homework Statement

Suppose {A

_{i}| i [tex]\in[/tex] I} is an indexed family of sets and I does

equal an empty set. Prove that [tex]\bigcap[/tex] i [tex]\in[/tex] I Ai

[tex]\in[/tex] [tex]\bigcap[/tex] i[tex]\in[/tex] I P(Ai ) and P(Ai) is the

power set of Ai

## Homework Equations

none

## The Attempt at a Solution

Suppose x [tex]\in[/tex] {A

_{i}| i [tex]\in[/tex] I}. Let i be an arbitrary element of

I where x [tex]\in[/tex] Ai . Then let y be an arbitrary element of x. Since x

is an element of Ai and y [tex]\in[/tex] x it follows that ...

maybe i want to show that [tex]\bigcap[/tex] i [tex]\in[/tex] I Ai [tex]\subseteq[/tex] [tex]\bigcap[/tex] i [tex]\in[/tex] I Ai and then

I could say that [tex]\bigcap[/tex] i [tex]\in[/tex] I Ai [tex]\in[/tex] [tex]\bigcap[/tex] i[tex]\in[/tex] I P(Ai )