2. (4 points) Let K and L be two nonempty compact subsets of R. Prove that there exist on E K and bo E L such that loo - bo| = inf {la- b| : 0 6 K, be L}. Prove that there exist a, ( K and b, E L such that (a, -b, | = sup{la-b| : 0 6 K, be L}