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Let L be a regular language and M be a context-free language, both over the alphabet    denote the complements of  L and M respectively. Which of the following statements about the language 
  • a)
    It is necessarily regular but not necessarily context-free.
  • b)
    It is necessarily context-free.
  • c)
    It is necessarily non-regular.
  • d)
    None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let L be a regular language and M be a context-free language, both ove...
Proposition:
L is a regular language
M is a context free language
Derivation:
L_c  union M_c = complement{L intersection M}
Now, L intersection M is a CFL according to closure laws of CFLs, i.e. intersection of a CFL with RL is always a CFL.
But, complement{L intersection M} might not be a CFL because complement over CFL doesn’t guarantee a CFL. It can even be a RL or it might even lie outside the CFL circle. It will be a context-sensitive language certainly, but nothing else can be said about it.
Conclusion:
Considering the above derivation, none of the statements are true. Hence correct answer would be (D) None of the above.
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Let L be a regular language and M be a context-free language, both over the alphabet denote the complements of Land M respectively. Which of the following statements about the language a)It is necessarily regular but not necessarily context-free.b)It is necessarily context-free.c)It is necessarily non-regular.d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Let L be a regular language and M be a context-free language, both over the alphabet denote the complements of Land M respectively. Which of the following statements about the language a)It is necessarily regular but not necessarily context-free.b)It is necessarily context-free.c)It is necessarily non-regular.d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let L be a regular language and M be a context-free language, both over the alphabet denote the complements of Land M respectively. Which of the following statements about the language a)It is necessarily regular but not necessarily context-free.b)It is necessarily context-free.c)It is necessarily non-regular.d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let L be a regular language and M be a context-free language, both over the alphabet denote the complements of Land M respectively. Which of the following statements about the language a)It is necessarily regular but not necessarily context-free.b)It is necessarily context-free.c)It is necessarily non-regular.d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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