GATE CS 2023 Set 1 — Question 24
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Theory of Computation → Context-Free Languages → Closure Properties (CFL)
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Question
Which of the following statements is/are CORRECT?
Correct answer
(A) The intersection of two regular languages is regular.; (C) The intersection of two recursive languages is recursive.; (D) The intersection of two recursively enumerable languages is recursively enumerable.
Solution
Closure properties under intersection for various language families are as follows:
- Regular Languages: Closed under intersection. (Statement A is correct)
- Context-Free Languages (CFLs): NOT closed under intersection. For example, and are both CFLs, but their intersection is not a CFL. (Statement B is incorrect)
- Recursive Languages: Closed under intersection. (Statement C is correct)
- Recursively Enumerable (RE) Languages: Closed under intersection. (Statement D is correct)
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