Decide which of the following statements are true and which are false. Prove the true ones and

Question:

Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones.
a) If A and B are nonempty, bounded subsets of R, then sup(A ∩ B) < I sup A.
b) Let ε be a positive real number. If A is a nonempty, bounded subset of R and B = {εx: x ∈ A), then sup(B) = ε sup(A).
c) If A + B: = {a + b : a ∈ A and b ∈ B), where A and B are nonempty, bounded subsets of R, then sup(A + B) = sup(A) + sup(B).
d) If A - B: = {a - b : a ∈ A and b ∈ B}, where A and B are nonempty, bounded subsets of R, then sup(A - B) = sup(A) - sup(B)