1. Not finding help here? Sign up for a free 30min 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!

Indexed Family fo Subsets

  1. Sep 3, 2008 #1
    1. The problem statement, all variables and given/known data

    Let f: A [tex]\rightarrow[/tex] B be given and let {X[tex]_{\alpha}[/tex]} for [tex]\alpha[/tex] [tex]\in[/tex] I be an indexed family of subsets of A.


    Prove:

    a) f(U[tex]_{\alpha\inI}[/tex] X[tex]_{\alpha}[/tex]) = U[tex]_{\alpha\inI}[/tex]f(X[tex]_{\alpha}[/tex])



    3. The attempt at a solution

    To prove these two things are equal I must show that the left side is a subset of the right and that the right side is a subset of the left. However, the notation on these problems is really confusing me. I understand that I am being asked to show that the function f applied to the union of all the X[tex]_{\alpha}[/tex] s is equal to the union of what you get after you apply the function f to the X[tex]_{\alpha}[/tex]s. And the result seems reasonable to me, but I have no idea how to right this out.

    There are actually many more parts to this question, but I think I will be able to do them once I understand how to write things out.

    (I had a hard time getting the symbols to type in right, so I am including a scanned version of the problem as well. Thanks.)
     

    Attached Files:

  2. jcsd
  3. Sep 3, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi pezola! :smile:

    (you have to leave a space after \in :wink:)

    Hint: start "if y ∈ f([tex]\bigcup_{\alpha\in I}X_{\alpha}[/tex]), then ∃ x ∈ [tex]\bigcup_{\alpha\in I}X_{\alpha}[/tex] such that f(x) = y, so ∃ … " :smile:
     
  4. Sep 5, 2008 #3
    It is amazing the difference a space will make. :biggrin:

    Thank you so much!...I was able to do all parts of the problem and even presented them in class!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Indexed Family fo Subsets
  1. Limit fo integral (Replies: 7)

Loading...