- #1

SMA_01

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**Characteristic function and preimage?**

## Homework Statement

Let S be a nonempty subset of ℝ.

Define χ

_{s}= { 1 if x is in S and 0 if x is not in S

Determine χ

_{s}

^{-1}(Q) [where Q=set of all rational numbers]

and χ

_{s}

^{-1}((0,∞))

We haven't really dealt much with this function, and I really don't know how to go about doing this. I'm guessing for Q it will be all x in S such that f(x)=Q? Is that right?

Any help is appreciated,

Thanks.