in Theory of Computation
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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 $p^*q^*$ and $Q$ be $\{p^nq^n \mid n \in N\})$. Then which of the following is ALWAYS regular?

  1. $P \cap Q$
  2. $P-Q$
  3. $\Sigma^*-P$
  4. $\Sigma^*-Q$
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