Summation Properties of Big Omega
Essentially, anything you can prove for $O(-)$ has a closely related fact that you can prove for $\Omega(-)$, in essentially the same way.  By "closely related", I mean that you might have to swap $\geq$ and $\leq$ and things like that.

You can check that the following is a counterexample to your statement about $a$, $b$ and&nbsp;$c$.
\begin{align*}
    a(x) &amp;= \begin{cases}x&amp;\text{if $x$ is even}\\0&amp;\text{if $x$ is odd}\end{cases}\\
    b(x) &amp;= \begin{cases}0&amp;\text{if $x$ is even}\\x&amp;\text{if $x$ is odd}\end{cases}\\
    c(x) &amp;= x\,.
\end{align*}