pshah01
September 23rd, 2006, 05:41 PM
For each of the following two statements, decide whether it is true or false (do not forget to write this down). If it is true, prove it using any method you like. If it is false, provide a counterexample:
(a) For any three eventually positive functions f, g, and h, f(n) = O(g(n)) implies
f(n) + h(n) = O(g(n) + h(n)).
(b) For any two eventually positive functions f and g, f(n) = (g(n)) implies 2f(n) =(2g(m)).
(a) For any three eventually positive functions f, g, and h, f(n) = O(g(n)) implies
f(n) + h(n) = O(g(n) + h(n)).
(b) For any two eventually positive functions f and g, f(n) = (g(n)) implies 2f(n) =(2g(m)).