re and rec

Question

Consider a language L for which there exists a Turing machine that, when presented with any finite input string w over the alphabet, halts and accepts if ω ?  L, and halts and rejects otherwise. Which one of the following statements is/are TRUE?

• 1. 

  L is recursive but not recursively enumerable.

  

• 2. 

  L is recursively enumerable but not recursive.

  

• 3. 

  L is recursively enumerable.

  

• 4. 

  None of the above

Comments

3 ??

Answer 1

The language referring to the problem is a property of halting Turing Machine and hence the language is decidable(recursive)..In other words the problem given is membership problem for recursive language which is decidable and hence recursive..

And we know if a language is recursive then language will be recursively enumerable as well..

Hence C) is correct answer..