3-4 Asymptotic notation properties Let f (n) and g(n) be asymptotically positive functions. Prove or disprove each of a. f(n) = 0(g(n)) implies g(n) = 0(f(n)) b. f(n) +g(n)(min(f (n). g(n c. f(n) = 0(g(n)) implies lg(f(n)) = 0(lg(g(n))), where Ig(g(n)) 1 and f(n) 2 1 for all sufficiently large n. d, f(n) = 0(g(n)) implies 2f(n)-O (2 ) e, f(n) = 0((f(n))2). f, f(n) = 0(g(n)) implies g(n) = (f(n)). g, f (n) = (f(n/2)). I. f(n) + o(f(n))=6(f(n)). g (n)