I recently started learning about asymptotic notations. While I was doing practice questions (not HW) I found various question that stumped me totally. So I just want some pointers on how to go by solving these type of questions. So here is a basic question. Given the following,
If $f(n) = \Omega(h(n))$ and $g(n) = O(h(n))$ then $f(n) = \Omega(g(n))$.
How can I solve this and see if that is true or false. Here is what I have tried so far, I tried to use definitions of big-$O$ and big-$\Omega$ on $f(n)$, $g(n)$ and $h(n)$ and then combining those resulting equations to prove/disprove the outcome but I got confused.
So I need explanation of this solutions so I can make it more clear for myself. Any help would be appreciated.