(adsbygoogle = window.adsbygoogle || []).push({}); 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.)

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# Homework Help: Indexed Family fo Subsets

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