2. (30 points) 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 2f(n)=O(2g(n)). - (c) If g(n)=O(f(n)), then f(n)+g(n)=(f(n))