Difficult simply connected problem

This is a hard problem in my book ( marked with a star). I don't even see the
question in the problem. I guess it's the last sentence, but I still have no clue to
solve it. Hope someone can gives help.

Suppose $\Omega$ is a bounded region. Let $L$ be a (two way infinite) line that intersects $\Omega$. Assume that $\Omega\cap L$ is an interval $I$. Choosing an orientation for $L$, we can define $\Omega_l$ and $\Omega_r$ to be subregions of $\Omega$ lying strictly to the left or right of L, with $\Omega=\Omega_l \cup I \cup \Omega_r$ a disjoint union. If $\Omega_l$ a $\Omega_r$nd are simply connected, then $\Omega$ is simply connected.