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For any two languages L1 and L2 such that L1 is context free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?
1. L1' (complement of L1) is recursive
2. L2' (complement of L2) is recursive
3. L1' is context-free
4. L1' ∪ L2 is recursively enumerable
  • a)
    1 only
  • b)
    3 only
  • c)
    3 and 4 only
  • d)
    1 and 4 only
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For any two languages L1 and L2 such that L1 is context free and L2 is...
1. L1' (complement of L1) is recursive is true L1 is context free. Every context free language is also recursive and recursive languages are closed under complement. 4. L1' ∪ L2 is recursively enumerable is true Since L1' is recursive, it is also recursively enumerable and recursively enumerable languages are closed under union. Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive languages are recursively enumerable. (Source: Wiki) 3. L1' is context-free: Context-free languages are not closed under complement, intersection, or difference. 2. L2' (complement of L2) is recursive is false: Recursively enumerable languages are not closed under set difference or complementation
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For any two languages L1 and L2 such that L1 is context free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?1. L1' (complement of L1) is recursive2. L2' (complement of L2) is recursive3. L1' is context-free4. L1' ∪ L2 is recursively enumerablea)1 onlyb)3 onlyc)3 and 4 onlyd)1 and 4 onlyCorrect answer is option 'D'. Can you explain this answer?
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For any two languages L1 and L2 such that L1 is context free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?1. L1' (complement of L1) is recursive2. L2' (complement of L2) is recursive3. L1' is context-free4. L1' ∪ L2 is recursively enumerablea)1 onlyb)3 onlyc)3 and 4 onlyd)1 and 4 onlyCorrect 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 For any two languages L1 and L2 such that L1 is context free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?1. L1' (complement of L1) is recursive2. L2' (complement of L2) is recursive3. L1' is context-free4. L1' ∪ L2 is recursively enumerablea)1 onlyb)3 onlyc)3 and 4 onlyd)1 and 4 onlyCorrect 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 For any two languages L1 and L2 such that L1 is context free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?1. L1' (complement of L1) is recursive2. L2' (complement of L2) is recursive3. L1' is context-free4. L1' ∪ L2 is recursively enumerablea)1 onlyb)3 onlyc)3 and 4 onlyd)1 and 4 onlyCorrect answer is option 'D'. Can you explain this answer?.
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