For the following statements, consider the functions f(n), g(n) and constant c such that f(n) > 0, g(n) > 0, and c> 0. Indicate whether the statements are true or false. If true prove the statement by providing a formal argument based on the definition of asymptotic notation, otherwise, provide a counter-example to prove that they are false. (a) max{f(n), g(n)} = O(f(n) + g(n)). (61) f(n) +c= O(f(n)). (62) If f(n) > 1, then f(n) +c= O(f(n)). (ci) If f(n) = O(g(n)), log(f(n)) > 0 and log(g(n)) > 0, then log(f(n)) = O(log(g(n))). (c2) If f(n) = 0(g(n)), log(f(n)) > 0 and log(g(n)) > 1, then log(f(n)) = O(log(g(n))). (di) f(2n) = O(f(n)). (d2) If f(n) = O(n), then f(2n) = 0(n). (d3) If f(n) = O(n), then f(2n) = O(f(n))