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## Homework Statement

Let A and B be subsets of ℝ

^{n}with A

^{0}, B

^{0}denoting the sets of interior points for A and B respectively. Prove that A

^{0}[itex]\cup[/itex]B

^{0}is a subset of the interior of A[itex]\cup[/itex]B. Give an example where the inclusion is strict.

## Homework Equations

I know a point Q[itex]\in[/itex]S is an interior point of S if [itex]\exists N_δ(Q)[/itex] which is a subset of S.

## The Attempt at a Solution

I've never actually attempted a problem like this, I'm wondering where to start really. Do I assume the existence of a point in A

^{0}[itex]\cup[/itex]B

^{0}and then prove it is also contained within (A[itex]\cup[/itex]B)

^{0}? Any nudge in the right direction would be very helpful.