Which of the following statements is/are CORRECT?

A.

The intersection of two regular languages is regular.

B.

The intersection of two context-free languages is context-free.

C.

The intersection of two recursive languages is recursive.

D.

The intersection of two recursively enumerable languages is recursively enumerable.

Solution:
  • (A). Regular languages are closed under intersection.
    L1(regular) ∩ L2(regular) = L(regular)
    So, A is correct.
  • (B). Context-free languages are not closed under intersection and complement.
    So, B is incorrect.
  • (C). Recursive languages are closed under intersection.
    L1(recursive) ∩ L2(recursive) = L(recursive)
    So, C is correct.
  • (D). Recursive enumerable languages are also closed under intersection.
    So, D is also correct.

Refer to the Closure Properties table for similar questions.