Prove or disprove each of the following statements. a. n! = O(n^n) b. n^b = o(a^n) for any constant a > 1, b > 0 c. log^b n = O(n^a) for any constant a > 1, b > 0 log(n!) = theta(n log n) e. (n + a)^b = theta (n^b) where a, b elementof Real and b > 0