4. (20 pts) Write true or false to each of the following statements (a) If f(n) = n2+8, then f(n) e (n2) (b) If f(n) n2 8, then f(n) E O(n) (c) If f(n)-, 1, then f(n) e O(log n) (d) If f(n)- , then f(n) O(n log n) (e) If "f(n)-, 1, then f(n) e (n) (f) If f(n) O(n) and g(n) E O(n), then f(n) +g(n) E O(n) (g) If f(n) E O(n) and g(n) E O(n2), then f(n) +g(n) E O(n2) (h) If f(n) E 0(n) and g(n) E 0(), then f(n) + g(n) 0(n) (i) If f(n) E 0(n) and g(n) E (n), then f(n) + g(n) E (n) (j) If f(n) E 0(n), then nX f(n) e O(n*) (k) If f(n) E O(n) and g(n) E O(n2), then f(n) x g(n) E O(n3) (1) If f(n) E (n log n), then f(n) n E O(n2 log n) (m) If f(n) E (n log n) and g(n) E (n log n), then E (1) (n) If f(n) E 0(n) and g(n) E 0(), then lim n oo= 0 (o) If f(n) E (n) and g(n) E (n), then E 1 (p) If f(n) E (n) and g(n) E (n2), then lim,PS f -o (q) If f(n) E (n) and g(n) E (n), then E 1 (r) If f(n) E O(n) and limn oo n)-0, then g(n) (n) (s) lf f(n) E (n) and limn+20 gm = 0, then g(n) e (n) (t) f(n)+g(n) E (max f(n), g(n))