Let S and T be subsets of ℝ. Prove the following.
(a) int S is an open set.
(b) int (int S) = int S
(c) int (S ∩ T) = (int S) ∩ (int T)
(d) (int S) ∪ (int T) ⊆ int (S ∪ T)
(e) Find an example to show that equality need not hold in part (d).
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