Question

If L and L are recursively enumerable, then L is:

• A. Regular
• B. Context-free
• C. Context-sensitive
• D. Recursive

Hint:

To determine whether a language is recursive, check if both the language and its complement are recursively enumerable.

Answer 1

The Correct Option is D

If both L and L are recursively enumerable (RE), then L must be recursive. This is because a language L is recursive if both L and its complement L are RE. In other words, if you can enumerate both a language and its complement, you can decide membership in the language, meaning it is recursive.