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Let L1 be a recursive language, and let L2 be a recursively enumerable but not a recursive language. Which one of the following is true?
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- L1 is recursive and L2 is recursively enumerable
- L1 is recursive and L2 is not recursively enumerable
- L1 and L2 are recursively enumerable
- L1 is recursive enumerable and L2 is recursive
- L1 is recursive and L2 is recursively enumerable
Correct Option: B
The rules here used will be. All those languages which are recursive their complements are also recursive. So option (a) & (b) can be correct.
Now languages which are recursively enumerable but not recursive, their complements can't be recursively enumerable.
So only option (b) is correct. Hence (b) is correct option.
