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Which of the following statements is are true?
  • a)
    If L1 and L2 are regular, then L1 ∩ L2 must be DCFL.
  • b)
    Every subset of recursively enumerable Language is recursive
  • c)
    If Language L & its complement L are both recursively enumerable then  must be recursive
  • d)
    Complement of context free language must be recursive. 
Correct answer is option 'A,C,D'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is are true?a)If L1 and L2 are regul...
Option A: True 
If L1 and L2 are regular then L1 ∩ L2 is Regular thus also deterministic context free Language.
Option B: False
Since ∑* is a recursively enumerable Language but there are many languages which are subset of ∑* which are not Recursive.
Option C: True
If L is recursively enumerable Language, then for all member strings of L, the TM of L will halt within finite time. If  is recursively enumerable Language, then for all nonmember strings of L. The TM of  will halt within finite time. Thus for both member and nonmember strings of L and  we have a TM which halts within finite time. Thus L is a Recursive Language.
Option D: True
Complement of CFL is a CSL in the worst case which is Recursive.
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Which of the following statements is are true?a)If L1 and L2 are regular, then L1 ∩ L2 must be DCFL.b)Every subset of recursively enumerable Language is recursivec)If Language L & its complement L are both recursively enumerable then must be recursived)Complement of context free language must be recursive.Correct answer is option 'A,C,D'. Can you explain this answer?
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