a) State the definition of the fact that f (n) is O(g(n)), where f (n) and g(n) are functions from the set of positive integers to the set of real numbers.
b) Use the definition of the fact that f (n) is O(g(n)) directly to prove or disprove that n2 + 18n + 107 is O(n3).
c) Use the definition of the fact that f (n) is O(g(n)) directly to prove or disprove that n3 is O(n2 + 18n + 107).