Problem 2 [4+4+4+4=16 marks] For each pair of the following functions, fill in the correct asymptotic notation among O, 0, and w in the statement f(n) E U(g(n)). Prove the relationship using any relationship or technique that described in class. a) f(n) = n2 + 27n log n + 2020 versus g(n) = n log n + 2020 b) f(n) = 10M + 99n10 versus g(n) = 75" + 25n27 c) f(n) = Vn versus g(n) = (log n)? d) f(n) = log log n versus g(n) = (log log log n)8