Prove the following statements by using the definitions of the notations involved, or disprove them by giving a specific counterexample. All the functions are nonnegative functions defined on the set of natural numbers.

(a) If f(n) = O(g(n)), then g(n) = (f(n)).

(b) If f(n) = O(g(n)), then 2^f(n) = O(2^g(n) ).

(c) If g(n) = O(f(n)), then f(n) + g(n) = (f(n)