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

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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