EX1

Let f (n) and g(n) be asymptotically positive functions. Briefly prove or disprove each of the following conjectures.

1.1 f (n) = O(g(n)) implies g(n) = O(f (n)).

1.2 f (n) + g(n) = Θ(min(f (n), g(n))

1.3 f (n) = O(g(n)) implies g(n) = Θ(f (n)).

1.4 f (n) = Θ(f (n/2)).

 

EX2