1. (6 points) Assuming that fi(n) is O(gi(n)) and f2(n) is O(g2(n)): (Drozdek, p.71) a. (2 points) Prove that fi(n) + f2(n) is O(max(gi(n), g2(n)). b. (2 points) Prove that fi(n) * f2(n) is O(gi(n) * g2(n)). c. (1 point) Find a counterexample to refute that fi(n) - f2(n) is O(gi(n) - g2(n)). d. (1 point)Find a counterexample to refute that fi(n)/f:(n) is O(gi(n) /g2(n))