• Support PF! Buy your school textbooks, materials and every day products Here!

Set theory Proof help

  • Thread starter nike5
  • Start date
  • #1
13
0

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 )
 

Answers and Replies

  • #2
238
0
Let [tex]\left\{ A_{i} \right\}_{i \in I} [/tex] be your indexed set of family.

Do you mean this [tex]\bigcap_{i=1} A_i = \left\{ x : \forall i \in I: x \in A_i \right\} [/tex]?
 
  • #3
13
0
Yes sry about the horrible looking symbols
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,794
925

Homework Statement


Suppose {Ai| i [tex]\in[/tex] I} is an indexed family of sets and I does
equal an empty set.
Did you mean "does not equal and empty set"?
 
  • #5
13
0
I [tex]\neq[/tex] [tex]\oslash[/tex] is what I meant
 

Related Threads for: Set theory Proof help

  • Last Post
Replies
3
Views
3K
Top