Given f(n) = n^(2^(100)) and g(n) = [lg n]! find which of the following statements are true:

(i) f(n) = o(g(n))

(ii) f(n) = O(g(n))

(iii) f(n) = w(g(n))

(iv) f(n) = Omega(g(n))

(v) f(n) = Theta(g(n)).

"[x]" is the ceiling of x. "a^b" means a raised to the power b.