- #1
nike5
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Homework Statement
Suppose {Ai| 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] {Ai| 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 )