Let A and B be subsets of ℝn with A0, B0 denoting the sets of interior points for A and B respectively. Prove that A0[itex]\cup[/itex]B0 is a subset of the interior of A[itex]\cup[/itex]B. Give an example where the inclusion is strict.
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 A0[itex]\cup[/itex]B0 and then prove it is also contained within (A[itex]\cup[/itex]B)0 ? Any nudge in the right direction would be very helpful.