Given nonempty subsets A and B of positive real numbers, define A) Show that sup(A B) = (sup A)(sup B).

B) Show that

C) Show that, if A and B are bounded subsets of real numbers, then sup (A - B) = max {(sup A)(sup B), (sup A)(inf B), (inf A)(sup B), (inf A)(inf B)}.

D) Give an example of two nonempty bounded sets A and B for which sup(A B) (sup A)(sup B)