ANSWER ALL 3 PARTS PLEASE

We present another asymptotic notation that is used in the analysis of algorithms: For functions f,g, we say f=o(g) (" f is little- o of g ") if and only if the ratio g(n)f(n) goes to zero as n tends to infinity. For example, logn=o(n) but n=o(n). 1. Is n=o(n) ? Briefly explain why. 2. Is it possible that f=o(g) and g=O(f) ? If yes, give an example. Otherwise prove that it is not possible. 3. Show that the worst case number of comparisons needed to merge two sorted lists, each of size n, is at least 2no(n). (Hint: In how many ways can we write down 2n numbers as two sorted lists of n numbers each