math question on sets?

Question

Please find a counterexample to the following:
note: S and T are subsets of R (set of all real numbers)

1. if set S is closed, then the closure of the interior of S = S

2. bd ( cl S ) = bd S

3. bd ( S union T ) = ( bd S ) union (bd T)

thanks so much

Answer 1

3. Let S = [0,2] and T = [1,3].

Answer 2

1. S = {0}, int (S) = ∅, cl (int (S)) = ∅ ≠ S, even though {0} is closed
2. S = ℚ, ∂(cl (S)) = ∂ℝ = ∅ ≠ ℝ = ∂S
3. S=ℚ, T=ℝ\ℚ, ∂(S∪T) = ∂ℝ = ∅ ≠ ℝ∪ℝ = ∂S ∪ ∂T