I am trying to proof the properties of the complement and concatenation of two non-context-free languages $L_1$ and $L_2$.
I believe that both of these languages are closed under complement and concatenation but can't seem to find a solid proof for it. I'm leaning towards them being closed because I can't find any counter examples.
I already proved that non-context-free languages are not closed under union and intersection, so I can use those properties (if applicable).
So in short what I want to proof, given $L_1, L_2$ are non-context-free languages:
$L_1L_2 \in S_{nonContextFree}$
$\overline{L_1} \in S_{nonContextFree}$