(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

When f: A -> B and S ⊆ B, we definte I_{f}(S) = { x ∈ A: f(s) ∈ S}. Let X and Y be subets of B.

a) Determine whether must equal I_{f}(X) ∪ I_{f}(Y).

b) Determine whether I_{f}(X ∩ Y) must equal I_{f}(X) ∩ I_{f}(Y).

2. Relevant equations

The definition of an inverse image is stated in the problem.

3. The attempt at a solution

So far I have tried to draw the schematic representation of the problem and didn't really get anything out of that.

Then I tried messing around with some proofs by saying "Choose an arbitrary x in I_{f}(X ∪ Y). Then, x = f(a) for some a in X ∪ Y." And then from there are I start questioning myself and don't know if I should continue/where I should go.

Thanks

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# Homework Help: Prove inverse image of function

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