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L1 is a Recursive Lang. and L2 is Recursively Enumerable but not Recursive. Which one is true?

a) (L1 Complement) is recursive and (L2 Complement) is Recursively Enumerable

b) (L1 Complement) is recursive and  (L2 Complement) is not Recursively Enumerable

c) (L1 Complement) is not recursive and (L2 Complement) is not Recursively Enumerable

d)  (L1 Complement) is recursive and (L2 Complement) is Recursive

1 Answer

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option b is true. Since, Recursive Language is closed under complement and Recursive enumerable but recursive is not closed under complement operation.

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