Exercise 1: f = O(g) is defined for asymptotically nonnegative functions f and g (both from N to N) to mean that there exist positive constants no and c such that: 05 f(n) no. For each of the following statements either prove the statement if it is true or otherwise provide a counter- example and justify why your counter-example is indeed a counter-example: 1. If f(n) = g(n), then f(n) = O(g(n)) 2. If f(n) > g(n), then f(n) + 0(g(n)) 3. If f = 0(g) then g=0(f). 4. If f = 0(g) and g=0(h) then f = 0(h). 5. If f = 0(g) and g = O(f) and Vn, f(n) > g(n) then f -g=0(1). 6. If f = 0(g) and g = O(f) then f = 0(1). 9 7. If f = 0(g) and h = 0(g) then f = O(h)