4. (10 pts) Write true or false to each of the following statements. (a) If f(n) = n2 + 8, then f(n) E O(ng). (b) If f(n) = D=1 }, then f(n) O(n log n). (c) If f(n) E O(n?) and g(n) E O(n), then f(n) + g(n) E O(na). (d) If f(n) E O(n^), then n x f(n) E O(n^). (e) If f(n) E O(n) and g(n) E O(n), then f(n) x g(n) E O(n^). (f) If f(n) O(n log n), then f(n) x n O(n log n). (g) If f(n) E O(n?) and g(n) O(n^), then limn700 film) e O(1). (h) If f(n) E O(n?) and g(n) E N(n2), then limn700 E O(1). (i) If f(n) O(na) and g(n) O(n?), then limn 400 (m) 0(1). (j) f(n) + g(n) (max f(n), g(n)). gn)