Hi, I'm in an intro topology course and need help proving these statements using balls.

1) Prove for any set S that Interior(S) = Complement of (Closure of S Complement)

2) Prove that if A ⊆ B then Interior(A) ⊆ Interior(B)

3) Prove that if A ⊆ B then Closure(B Complement) ⊆ Closure(A Complement)

Thanks a lot!