------------------------------------------------------------------------------ R-4.23) show that if d(n) is O(f(n)) and e(n) is O(g(n)) then d(n) - e(n) is not necessarily O(f(n) - g(n)) Example for when d(n) - e(n) is O(f(n) - g(n)) d(n) = 2n + 3 e(n) = 2n + 5 f(n) = 2n + 3n = 5n. C = 5, O(g(n)) is O(n) g(n) = 2n + 5n = 7n. C = 7, O(g(n)) is O(n) (2n + 3) - (2n + 5) is O(n - n) -2 is O(1) Example for when d(n) - e(n) is not O(f(n) - g(n)) d(n) = 10n e(n) = n d(n) is O(n) e(n) is O(n) d(n) - e(n) is? O(n - n) 10n - n is? O(1) O(n) is not O(1)