Proving asymptotic notations for functions
The first thing to do is to try to develop an intuition for whether the claim is true or false. Very roughly, $f=\Omega(h)$ says that $f$&nbsp;is bigger than&nbsp;$h$, and $g=O(h)$ says that $g$&nbsp;is smaller than&nbsp;$h$.  In both of those statements, "bigger" really means "at least as big as" and I've left off the conditions of "up to a constant factor" and "for large enough inputs".

So, if $f$&nbsp;is bigger than&nbsp;$h$ and $g$&nbsp;is smaller than&nbsp;$h$, is $f$ bigger than&nbsp;$g$? Intuitively, it ought to be. Since we've simplified, we might have gone wrong, but our intuition is that we should try to prove that the statement is true, rather than trying to find a counterexample.

Apply the definitions and you get that (try it on your own, first!)...


   ... there are constants $c$ and&nbsp;$d$ such that, for all large enough&nbsp;$n$, $f(n)\geq c\,h(n)$ and $g(n)\leq d\,h(n)$. Therefore, $f(n)\geq \tfrac{c}{d}g(n)$ for all large enough&nbsp;$n$, which is to say that $f=\Omega(g)$.