(b) [15 points] Assume that you have two functions f(n) and g(n) such that f(n) = O(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) (i) log2 f (n) is O(log2 9(n)), under the assumptions of f(n) 2 1 for all n, and log2 g(n) 2 1 for all n. i) 2/ is 0 (2 ) f(n) is O (g(n)2), under the assumptions of f(n) 2 1 for all n, and log2 g(n 2 1 for all n