4. (10 pts) Write true or false to each of the following statements. (a) If f(n) = n? +8, then f(n) E 0(n). (b) If f(n) = E, then f(n) E O(n log n). (c) If f(n) E O(n) and g(n) E O(n), then f(n) + g(n) e O(n). (d) If f(n) E O(n), then n 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) E O(n log n), then f(n) x n O(n log n). (n) g(n) E O(1). (g) If /() O(n?) and g(n) (?), then lim, f(n) g(n) (h) If f(n) E O(n2) and g(n) E N(n), then lim, 0 (1). f(n) (1). (i) If f(n) E O(n) and g(n) E O(n), then lim, p00 G) /m) + 9(n) (max /(n),9(n))