Prove or disprove each of the following statements.

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

f(n) + g(n) = (min f (n), g(n))

f (n) =O (g(n)) implies lg(f(n)) = O(lg(g(n))), where lg(g(n)) >= 1 and f(n) >= 1 for all sufficiently large n.

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