In the class we have seen three equivalent definitions for f(n)=O(g(n)). The first of these was: f(n) = O(g(n)) if and only if there is some constant C > 0 as well as a positive integer threshold n0 such that for every n > n0 we have f(n) < Cf(n). () (A) Show that under the mild assumption that f(n)1 for all n >0, the above condition is equivalent to: f(n)=O(g(n)) if and only if there is some constant C >0 such that for every n >0 we have f(n) 0, then () is not equivalent with (). For this you need to give an example for f and g (however pathologic it is), where () holds but () does not.