I need to do an exercise with different questions about the length of languages in theoretical computer science. I got stuck at the first one and don't know how to construct the following.
Let $\ L_1$ and $\ L_2$ be two non-empty languages over an alphabet $\Sigma$ with length of $\ L_1$ equal to $\ k$ and length of $\ L_2$ equal to $\ l$. Give for every $\ k \ge 1$ and an alphabet of your choice an example of $\ L_1$ and $\ L_2$ such that $\ |L_1 \cdot L_2 | = k+1$.
Hope for help, thanks a lot