Let f(n) and g(n) be two functions from N+ to R+. Prove or disprove the following assertions. To disprove, you only need to give a counter example for functions f(n)
and/or g(n) which make the assertion false.
(a) O(O(f(n))) = O(f(n))
(b) O((f(n))) = O(f(n))
(c) (O(f(n))) = (f(n))
(d)
(O(f(n))) = O(
(f(n)))
(e) If f(n) = (h(n)) and g(n) = (h(n)), then f(n) + g(n) = (h(n))
(f) If f(n) = (g(n)), then 2f(n) = (2g(n))
(g) f(n) + g(n) = (min(f(n) + g(n)))