4. (20 pts) Write true or false to each of the following statements (a) If f(n)-n't 8, then f(n) E 6( ) (b) If f(n)- +8, then f(n) E 0(n*) (c) If f(n)- l, then f(n) 0(log n) (d) If f(n)- , then f(n) E 0(n log n) (e) If f(n) - f(n) E (n) (f) If f(n) E O(n) and g(n) E O(n), then f(n) +g(n) E O(n) (g) If f(n) E 0(n) and g(n) E 0(n2), then f(n) + g(n) E O(n2) (h) If f(n) EO(n) and g(n) E O(n2), then f(n) +g(n) E O(n) (i) If f(n) E 0(n) and g(n) E (n), then f(n) + g(n) E (n) G) If f(n) E O(n), then n2 x 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(n) (1) If f(n) E (nlogn), then f(n) X nE O(n2 log n) (m) lf f(n) E (n log n) and g(n) E (n logn), then f E (1) (n) lf f(n) 0(n) and g(n) 0( 2), then linn )*)(n-0 (o) lf f(n) 62(n) and g(n) E (n), then g(n) -1 (p) If f(n) E e(m) and g) E (2), then li0 (q) If f(n) E (n) and g(n) E (n), then 1. (r) lf f(n) E 0(n) and lim n oo -0, then gin) E (n) (s) If f(n) (n) and lim, 100 g(r1-0, then g(n) (n) (t) f(n)+g(n) E (max f(n), g(n)) Ili >00 g(n) g(TI) 00 g(n n)