CSE310 Asymptotic notation true false

ts) Write true or false to each of the following statements (a) If f(n)- 2 + 8, then f(n) E 6( ) (b) If f(n) 8, then f(n) E O(n). (c) If f(n) = then f(n) E O(log n) (d) If f.(n) = | , then f(n) e o(n log n) (e) If f(n)- , then f(n) (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 O(n) and g(n) E O(n2), then f(n) +g(n) E O(n2) (h) If f(n) E O(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) (n), then f(n) + g(n) (n) (G) If f(n) E O(n),then n2 x f(n) E O(n3) (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 logn), then f(n) n e(logn) (m) If f(n) E e(n log n) and g(n) E e(n log n), then 20 ) (n) If f(n) e 0(n) and 9(n) e 0(), then limnoo g(n)-0 (o) If f(n) e (n) and g(n) e (n), then g( ) E 91 (p) If f(n) e (n) and g(n) e (n2), then limn oom-0 (q) If f(n) E (n) and 9(n) E (n), then g(n) 91 (r) If f(n) E 0(n) and limn-w g(n) = 0, then g(n) 22(n) (s) If f(n) E (n) and lim n-wg(n)-0, then g(n) (n). (t) f(n) +g(n) E e(max f (n), g(n)