4. Let f(n) and g(n) be functions that take on positive values for all n > 1 and such that f(n) = 0(g(n)). Prove or give a counterexample to the following statements: (a) 2+1 0(2") (b) 22n= 0(2") (c) 3 O(2") (d) f(n) = (f(n/2)) (e) f(n) 0(g(n)) implies g(n)-9(f(n)) (f) log2 f(n)=0(log29(n)) (g)2m)O(29m)) (h) f(n) O(g(n)2)