Give an example case for which all the three conditions

f(n)!= O(g(n)),

f(n)!= Theta (g(n)) and

f(n)!= Omega (g(n))

holds true.

We can say oscillating representation , i.e. sinx or cos x can hold true for this question. But will it be irreflexive relation? and It is not a non-negative function too. So, what other example is possible for it??