Asymptotic Notation closed

Question

Let f(n), g(n) & h(n) be 3 non-negative functions defined as follows:

$f(n) = O(g(n))\; \; \; g(n) \neq O(f(n))$

$g(n) = O(h(n))\: \: \: h(n) = O(g(n))$

Which of the following is false?

(A). f(n) + g(n) = O(h(n))
(B). f(n) = O(h(n))
(C). $h(n) \neq O(f(n))$
(D). $f(n).h(n) \neq O(g(n).h(n))$

Comments

Option D) is the correct answer

consider the scenario

f(n)=n,g(n)=n^2.h(n)=n^3...so for these functions option d) is violating