Problem 8 (extra credit 10 points) Let f(n) and g(n) be asymptotically positive functions. Prove or disprove the following conjectures: (a) f(n)=O(g(n)) implies g(n)=O(f(n)) (b) f(n)+g(n)=(min(f(n),g(n))) (c) f(n)=O(g(n)) implies 2f(n)=O(2g(n)) (d) f(n)=(f(n/2))