Multiple choice

Nobody knows yet if P = NP. Consider the language L defined as follows.

$$L = \begin{cases} (0 +1)^* \text { if } (P = NP) \in E \\ \phi \text{ otherwise} \end{cases}$$

Which of the following statements is true?

  1. L is recursive

  2. L is recursively enumerable but not recursive

  3. L is not recursively enumerable

  4. Whether L is recursive or not will be known after we find out if P = NP

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A Correct answer
Explanation

A language L is said to be recursive if there exists any rule to determine whether an element belong to language or not, if language can be accepted by turning machine. So there exist the rules so L is recursive.