Assume that $f(n)$ and $g(n)$ are asymptotically positive. Which of the following is correct?

If $f(n)=O(g(n))$ and $g(n)=O(h(n))$, then by transitivity:

$f(n)=O(h(n))$

But option says:

$f(n)=\omega(h(n))$

So, option (a) is incorrect.

Check option (b):

If $f(n)=\Omega(g(n))$ and $g(n)=\Omega(h(n))$, then:

$f(n)=\Omega(h(n))$

But option says:

$f(n)=O(h(n))$

So, option (b) is incorrect.

Check option (c):

If $f(n)=o(g(n))$, then $f(n)$ grows strictly slower than $g(n)$.

If $g(n)=o(h(n))$, then $g(n)$ grows strictly slower than $h(n)$.

Therefore, $f(n)$ also grows strictly slower than $h(n)$.

So,

$f(n)=o(h(n))$

Thus, option (c) is correct.

Check option (d):

If $f(n)=\omega(g(n))$ and $g(n)=\omega(h(n))$, then:

$f(n)=\omega(h(n))$

Since $\omega(h(n))$ is stronger than $\Omega(h(n))$, option (d) is also mathematically correct.

Therefore, mathematically both option (c) and option (d) are correct.

If the exam expects only one answer, then the question has ambiguity.