For any language $L \subset \Sigma^*$, define $S(L)$ to be $$\{x\in L \mid \neg \exists y \in L: \exists z \in \Sigma^*: (z \ne \epsilon) \land (x=yz)  \}$$Show that $S(L) = S(S(L))$I'm confused about the question here. The way we define $S(L)$ takes elements from $L$ $(x \mid x \in L)$, but $x=yz$ and $y \notin L$. How is it possible for x to concatenate an element from $\bar{L}$ (complement of $L$ since $y \notin L$) and still be an element of $L$?
How do I interpret this question?
regular languages