Which of the following statements are TRUE gate computer science 2013

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Which of the following statements are TRUE? -gate-computer science-2013

Which of the following statements are TRUE?
 (1) The problem of determining whether there exists a cycle in an undirected graph is in P.
 (2) The problem of determining whether there exists a cycle in an undirected graph is in NP.
 (3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time
algorithm to solve A.
 (A) 1,2 and 3 (B) 1 and 2 only (C) 2 and 3 only (D) 1 and 3 only 



By:Amogh

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Answers

(A) 1,2 and 3 
Explanation: 1 is true because cycle detection can be done in polynomial time using DFS (See this).
2 is true because P is a subset of NP.
3 is true because NP complete is also a subset of NP and NP means Non-deterministic Polynomial time solution exists.

Aparna-Dasgupta

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