Let L1 be regular language, L2 be a deterministic context free language and L3…
2017
Let L1 be regular language, L2 be a deterministic context free language and L3 a recursively enumerable language, but not recursive. Which one of the following statements is false? , ISRO 2017
- A.
L3 ∩ L1 is recursive
- B.
L1 ∩ L2 ∩ L3 is recursively enumerable
- C.
L1 ∪ L2 is context free
- D.
L1 ∩ L2 is context free
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Correct answer: A
Given L1 is regular, L2 is DCFL, and L3 is RE but not recursive. We evaluate the closure properties. Regular languages are closed under intersection with themselves, but intersecting a non-recursive RE language (L3) with a regular language (L1) does not guarantee the result is recursive. For instance, if L1 = Σ*, then L3 ∩ L1 = L3, which is not recursive. Thus, the statement claiming L3 ∩ L1 is recursive is false.