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Indexed Collection of Sets

  • #1

Homework Statement


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]

Homework Equations


None


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?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #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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