.(I know this a CLRS question ... but I AM not able to understand the solution. So kindly give an elaborate and detailed solution)

3-5 variations on o and S2 Some authors define S2 in a slightly different way than we do; let's use S (read omega infinity") for this alternative definition. We say that f (n) S (g(n) if there exists a positive constant c such that f(n) z cg(n) 2 0 for infinitely many integers n a. Show that for any two functions f(n) and g (n) that are asymptotically nonneg- ative, either f (n) o g(m) or f (n) Gg (n)) or both, whereas this is not true if we use S2 in place of S2