GATE CS 2022 Set 1 — Question 48
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Theory of Computation → Context-Free Languages → Closure Properties (CFL)
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Question
Consider the following languages:Which of the following statements is/are FALSE?
Correct answer
(B) Neither L₁ nor L₂ is context-free.; (C) L₂, L₃ and L₂ ∩ L₃ all are context-free.; (D) Neither L₁ nor its complement is context-free.
Solution
Analyze the languages:
(A) True. is not CFL. are DCFL.
(B) False. IS context-free.
(C) False. is not context-free.
(D) False. The complement of IS context-free.The question asks for FALSE statements.
- is a standard example of a Context-Sensitive Language that is NOT Context-Free. However, its complement IS Context-Free.
- involves matching 's and 's while 's can be anything. This is a Deterministic Context-Free Language (DCFL).
- involves matching 's and 's while 's can be anything. This is also a DCFL.
- , which is NOT Context-Free.
(A) True. is not CFL. are DCFL.
(B) False. IS context-free.
(C) False. is not context-free.
(D) False. The complement of IS context-free.The question asks for FALSE statements.
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