a) State the definition of the fact that f(n) is O(g(n)), where f(n) and g(n) arc 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).

Solution: Step 1 : (a)Let and be function. and we say that is and there are constants C and KSuch that whenever Other ward the definition that is says that some fixed multiple of as grows bound.Step 2 : (b)is Consider Choose Then Choose C=126Note that < And =is Because =