1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Set theory Proof help

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data
    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
    2. Relevant equations

    3. 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 )
  2. jcsd
  3. Apr 30, 2009 #2
    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]?
  4. Apr 30, 2009 #3
    Yes sry about the horrible looking symbols
  5. Apr 30, 2009 #4


    User Avatar
    Science Advisor

    Did you mean "does not equal and empty set"?
  6. Apr 30, 2009 #5
    I [tex]\neq[/tex] [tex]\oslash[/tex] is what I meant
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook