(b) [15 points] Assume that you have two functions f(n) and 9(n) such that f (n) = 0(g(n)). For each of the following statements, decide whether you think it is true or false and accordingly give a proof (if true) or a counter-example (if false). (o) log, f(n) is O(log,9(w), under the assumptions or all n (i) 2T) is o (2") (iii) f(n) is O (g(n)2), under the assumptions of f(n)1 for all n, and log2 g(n)1 for all n. 29(n)