Consider an algorithm with inputs of size M and N. Though you dont know the exact relationship between M and N, you can be sure that 0 M N^2 . Prove (using the formal definitions of asymptotic notations) or disprove (by counterexample) each of the following:

(a) M + N^2 = O(M)

(b) N^2 log M^2 = O(N^2 log N)

(c) M log N + N log M = O(M log N)