GATE | GATE CS 2012 | Question 4

Assuming P != NP, which of the following is true ?
(A) NP-complete = NP
(B) NP-complete \cap P = \Phi
(C) NP-hard = NP
(D) P = NP-complete

(A) A
(B) B
(C) C
(D) D

Answer: (B)


The answer is B (no NP-Complete problem can be solved in polynomial time). Because, if one NP-Complete problem can be solved in polynomial time, then all NP problems can solved in polynomial time. If that is the case, then NP and P set become same which contradicts the given condition.

Related Article:
NP-Completeness | Set 1 (Introduction)
P versus NP problem (Wikipedia)

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