Question

Let P be a regular language and Q be a context-free language such that $Q\subseteq P$. (For example, let P be the language represented by the regular expression $P^{\ast }{q}^{\ast }$ and Q be $\{p^n{q}^n\mid nϵN\}$ Then which of the following is ALWAYS regular ?

Answer 1

${\sum }^{\ast }-P=P^c$

If P is regular. then $P^c$ is also regular, since regular language is closed under complementation.