Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures. - f(n)=O(g(n)) implies g(n)=O(f(n)). - f(n)=O(g(n)) implies log(f(n))=O(log(g(n))), where log(g(n))>1 and f(n)>1 for all sufficiently large n. - f(n)+g(n)=(min(f(n),g(n))). - f(n)=O((f(n))2)