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Homework Help: 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

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    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!
     
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