- #1

- 13

- 0

## 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?