GATE Exam > GATE Questions > Which of the following statements is incorrec...
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Which of the following statements is incorrect ?
- a)Union of two DCFL is a CFL.
- b)Complementation of a regular language is a regular language.
- c)Turing recognizable languages are closed under intersection.
- d)None.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following statements is incorrect ?a)Union of two DCFL is...
Explanation:
Statement 1 is correct because union of two DCFL may or may not be DCFL but
surely CFL. Statement 2 is correct because regular languages are closed under complementation. Statement 3 is correct because Turing recognizable languages or recursive enumerable languages are closed under intersection.
Most Upvoted Answer
Which of the following statements is incorrect ?a)Union of two DCFL is...
Union of two DCFL is a CFL:
This statement is correct. The union of two deterministic context-free languages (DCFL) is a context-free language (CFL). This is because the union operation preserves the context-free property.
Complementation of a regular language is a regular language:
This statement is correct. The complement of a regular language is also a regular language. This is because regular languages are closed under complementation.
Turing recognizable languages are closed under intersection:
This statement is incorrect. Turing recognizable languages are not closed under intersection. This means that the intersection of two Turing recognizable languages may not necessarily be Turing recognizable. This is in contrast to context-free languages, which are closed under intersection.
Therefore, the correct answer is option 'D'.
This statement is correct. The union of two deterministic context-free languages (DCFL) is a context-free language (CFL). This is because the union operation preserves the context-free property.
Complementation of a regular language is a regular language:
This statement is correct. The complement of a regular language is also a regular language. This is because regular languages are closed under complementation.
Turing recognizable languages are closed under intersection:
This statement is incorrect. Turing recognizable languages are not closed under intersection. This means that the intersection of two Turing recognizable languages may not necessarily be Turing recognizable. This is in contrast to context-free languages, which are closed under intersection.
Therefore, the correct answer is option 'D'.
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Which of the following statements is incorrect ?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer?
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