(30 pts) Answer each of the following questions AND justify your answer. (You can either use the definition of O, , or the limit approach discussed in class for your justification; if you believe a statement is not true, you may give a counter example).

(a) Is 2n log n = O(n)?

(b) Is 2n log n = (n)?

(c) Is 5n³ + n² + 4 = (n³)?

(d) Is 5 log₂n = (n)?

(e) If f (n) = (g(n)), then does it follow that f (n) + g(n) = O(g(n))?

(f) If f (n) = O(g(n)) then does it follow that g(n) = (f (n))?

(g) Find two functions f (n) and g(n) such that neither f (n) = O(g(n)) nor g(n) = O(f (n)). When you find the functions, justify that in fact they the condition stated.

I'm entirely new to Data Structures and Algorithms, so I could sure use some help on approaching these problems, and even a step-by-step solution.