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Indexed Collection of Sets

  1. Sep 11, 2012 #1
    1. The problem statement, all variables and given/known data
    For a real number r, define A[itex]_{r}[/itex]={r[itex]^{}2[/itex]}, B[itex]_{r}[/itex] as the closed interval [r-1,r+1], C[itex]_{r}[/itex] as the interval (r,∞). For S = {1,2,4}, determine
    (a) [itex]\bigcup[/itex][itex]_{\alpha\in S}[/itex] A[itex]{_\alpha}[/itex] and [itex]\bigcap[/itex][itex]_{\alpha\in S}[/itex] A[itex]{_\alpha}[/itex]
    (b) [itex]\bigcup[/itex][itex]_{\alpha\in S}[/itex] B[itex]{_\alpha}[/itex] and [itex]\bigcap[/itex][itex]_{\alpha\in S}[/itex] B[itex]{_\alpha}[/itex]
    (c) [itex]\bigcup[/itex][itex]_{\alpha\in S}[/itex] C[itex]{_\alpha}[/itex] and [itex]\bigcap[/itex][itex]_{\alpha\in S}[/itex] C[itex]{_\alpha}[/itex]
    2. Relevant equations
    None


    3. The attempt at a solution
    So far I've gotten that you plug S into A[itex]_{r}[/itex] to get 1, 4, 16 and for the second part in A, you would get 1, since that is the only place that the intersection happens.

    For B, i've gotten the closed intervals of [0,2], [1,3] and [3,5] and i'm thinking because [1,3], and [3,5] have one in common, and they also intersect at those two points?

    For C, I do not know where to begin, as I'm not even sure if I'm doing the rest of these right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 11, 2012 #2
    If I'm not mistaking, Ar has only one Element for each r, so what does that tell you about the intersection? What is the condition for an element to be in the intersection of sets?
    That keeping in mind, what does that tell you about the intersection of Br.
    As for Cr, well, can you imagine what Cr looks like on the number line?
     
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