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?

R is NP-complete
R is NP-hard
Q is NP-complete
Q is NP-hard

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 2 : R is NP-hard

The correct answer is option 2.

If the NP-Hard problem is reducible to another problem in polynomial time, then that problem is also NP-hard which means every NP problem can be reduced to this problem in polynomial time.
If Q is reducible to S in polynomial time, Q could be NP because all NP problems can be reduced to S. Since Q could be Np therefore Q could be P also as P is a subset of NP. Also, Q could be NPC because every NPC problem can be reduced to another NPC problem in polynomial time.

5 views Answered 2022-09-04 04:29

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