Let P be a regular language and Q be context-free language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be {pn qn | n ∈ N}). Then which of the following is ALWAYS regular?
(A) P ∩ Q
(B) P – Q
(C) ∑* – P
(D) ∑* – Q
(A)
A
(B)
B
(C)
C
(D)
D
Answer: (C)
Explanation:
1. P ∩ Q would be Q, due to the given fact that Q ⊆ P, hence context free but not regular.
2. P − Q = P ∩ Q might not even be a context free language, due to the closure properties of context free languages.
3. Σ∗ − P is equivalently complement of P, hence regular.
4. Σ∗ − Q is equivalently complement of Q, hence it might not even be a context free language.
Hence, option C is the correct answer
Quiz of this Question
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