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Equivalence Relation

Consider the ...

Question

Consider the following statements:
1. The complement of every Turning decidable language is Turning decidable.
2. There exists some language which is in NP but is not Turing decidable.
3. If L is a language in NP, L is turing decidable.
Which of the above statements is/are True?

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Solution

Statement 1: True, because decidable languages (REC) are closed under complement operation.
Statement 2: False, because $P ⫅ N P \subseteq R E C$ .
So every P and every NP language is decidable (REC).
Statement 3: True, every language in NP is decidable.

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