I have this problem that I can't seem to be able to wrap my head around, and I was wondering if there was someone here that could help me understand it.
Let $L_1$ be a regular language over $\{a, b, c\}$. We define
$\qquad L_2 = \{xy \in \{a, b, c\}^∗ \mid xay \in L_1 \vee xby \in L_1\}$.
For example, if $L_1 = \{a, abc, c\}$, then $L_2 = \{\lambda, ac, bc\}$. Prove that $L_2$ is a regular language.
I really don't understand what language $L_2$ is in the first place, which makes it very hard for me to prove its regularity...
Any help would really be appreciated!