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GATE | GATE-CS-2015 (Set 2) | Question 65

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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? (A) Only 2 (B) Only 3 (C) Only 1 and 2 (D) Only 1 and 3

Answer: (D)

Explanation:
1 is true: Complement of Turing decidable is Turing Decidable.

3 is true. All NP problems are Turing decidable 
   (See https://www.geeksforgeeks.org/np-completeness-set-1/)

2 is false:  The definition of NP itself says solvable in 
     polynomial time using non-deterministic Turing machine. 


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Last Updated : 28 Jun, 2021
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