Algorithms | NP Complete | Question 3

Let X be a problem that belongs to the class NP. Then which one of the following is TRUE?
(A) There is no polynomial time algorithm for X.
(B) If X can be solved deterministically in polynomial time, then P = NP.
(C) If X is NP-hard, then it is NP-complete.

(D) X may be undecidable.

Answer: (C)

Explanation: (A) is incorrect because set NP includes both P(Polynomial time solvable) and NP-Complete .
(B) is incorrect because X may belong to P (same reason as (A))
(C) is correct because NP-Complete set is intersection of NP and NP-Hard sets.
(D) is incorrect because all NP problems are decidable in finite set of operations.

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