Problem 3 (16 points) Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjoctures. a. f(n)+g(n)=(min(f(n),g(n))). b. f(n)=((n/2)). c. 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. d. f(n)=O(g(n)) implies g(n)=O(f(n))