Summation Properties of Big Omega What are the properties of summation with Big Omega? I have been looking online but cannot find any sources on summation with Big Omega, only for Big Oh. For example, my main inquiry is if this statement is true or not, If $a(x) + b(x) ∈ \Omega(c(x))$, then $a(x) ∈ \Omega(c(x))$ or $b(x) ∈ \Omega(c(x))$.
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*}