Problem 4. Let f(n) and g(n) be asymptotically positive functions (A function is asymp- totically positive if there exists an no such that f(n) > 0, for all n 2 no). Prove or disprove each of the following conjectures. a. f(n) O(g(n)) implies g(n) O(f(n)) b. f(n) + g(n)= (min(f(n), g(n))) c. f(n) = 0(g(n)) implies 2f(n) = 0(2g(n)) d. f(n) O(f(n))2) e, f(n)=(f(n/2))