Let S be an NP-complete problem. Q and R are other two problems not known to…

2017

Let S be an NP-complete problem. Q and R are other two problems not known to be NP. Q is polynomial time reducible to S and S is polynomial time reducible to R. Which of the following statements is true?

Answer: B. R is NP-hardSince S is NP-complete, every problem in the class NP reduces to S by definition. The given reduction S ≤p R implies that every problem in NP also reduces to…

  1. A.

    R is NP-complete

  2. B.

    R is NP-hard

  3. C.

    Q is NP-complete

  4. D.

    Q is NP-hard

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Correct answer: B

Since S is NP-complete, every problem in the class NP reduces to S by definition. The given reduction S ≤p R implies that every problem in NP also reduces to R, which satisfies the formal definition of an NP-hard problem. Since it is not known if R is in NP, we conclude R is NP-hard.

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