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A problem in NP is NP-complete if
- a)It can be reduced to the 3-SAT problem in polynomial time.
- b)The 3-SAT problem can be reduced to it in polynomial time.
- c)It can be reduced to any other problem in NP in polynomial time.
- d)Some problem in NP can be reduced to it in polynomial time.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A problem in NP is NP-complete ifa)It can be reduced to the 3-SAT prob...
3-SAT being an NPC problem, reducing NP problem to 3-SAT would mean that NP problem is NPC
Most Upvoted Answer
A problem in NP is NP-complete ifa)It can be reduced to the 3-SAT prob...
The Correct Answer is Option A: It can be reduced to the 3-SAT problem in polynomial time.
Explanation:
To understand why option A is the correct answer, we need to have a clear understanding of NP-completeness and reduction.
NP-completeness:
A problem is said to be NP-complete if it is in the set of NP problems and every other problem in NP can be reduced to it in polynomial time. In other words, if we can solve an NP-complete problem in polynomial time, we can solve all problems in NP in polynomial time.
Reduction:
Reduction is a technique used in computer science to convert one problem into another problem in such a way that a solution to the second problem can be used to solve the first problem. This reduction is done in polynomial time.
To prove that a problem X is NP-complete, we need to show two things:
1. X is in NP.
2. Every problem in NP can be reduced to X in polynomial time.
Option A: It can be reduced to the 3-SAT problem in polynomial time.
The 3-SAT problem is a well-known NP-complete problem. It is a special case of the Boolean satisfiability problem (SAT), where we have a Boolean formula in conjunctive normal form (CNF) with three literals per clause. The goal is to determine if there exists an assignment of truth values to the variables such that the formula evaluates to true.
If a problem Y can be reduced to the 3-SAT problem in polynomial time, it means that we can transform an instance of Y into an equivalent instance of 3-SAT such that a solution to the 3-SAT instance corresponds to a solution to the Y instance and vice versa.
If a problem X can be reduced to Y, and Y is NP-complete, then X must also be NP-complete. This is because if we can solve Y in polynomial time, we can solve X in polynomial time by first reducing X to Y and then applying the polynomial time algorithm for Y.
Therefore, if a problem is NP-complete, it can be reduced to the 3-SAT problem in polynomial time. Thus, option A is the correct answer.
Explanation:
To understand why option A is the correct answer, we need to have a clear understanding of NP-completeness and reduction.
NP-completeness:
A problem is said to be NP-complete if it is in the set of NP problems and every other problem in NP can be reduced to it in polynomial time. In other words, if we can solve an NP-complete problem in polynomial time, we can solve all problems in NP in polynomial time.
Reduction:
Reduction is a technique used in computer science to convert one problem into another problem in such a way that a solution to the second problem can be used to solve the first problem. This reduction is done in polynomial time.
To prove that a problem X is NP-complete, we need to show two things:
1. X is in NP.
2. Every problem in NP can be reduced to X in polynomial time.
Option A: It can be reduced to the 3-SAT problem in polynomial time.
The 3-SAT problem is a well-known NP-complete problem. It is a special case of the Boolean satisfiability problem (SAT), where we have a Boolean formula in conjunctive normal form (CNF) with three literals per clause. The goal is to determine if there exists an assignment of truth values to the variables such that the formula evaluates to true.
If a problem Y can be reduced to the 3-SAT problem in polynomial time, it means that we can transform an instance of Y into an equivalent instance of 3-SAT such that a solution to the 3-SAT instance corresponds to a solution to the Y instance and vice versa.
If a problem X can be reduced to Y, and Y is NP-complete, then X must also be NP-complete. This is because if we can solve Y in polynomial time, we can solve X in polynomial time by first reducing X to Y and then applying the polynomial time algorithm for Y.
Therefore, if a problem is NP-complete, it can be reduced to the 3-SAT problem in polynomial time. Thus, option A is the correct answer.
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Community Answer
A problem in NP is NP-complete ifa)It can be reduced to the 3-SAT prob...
Sir,,, I m confused ,, for me answer d is, correct.....
reason
a probllem is said to be np complete if
a) if it is np hard
b) if it is in np
in question it is given tha it is in np
so 2nd condition is met for being np complete
by option d 1st condition also matches as some problem can be redused to it so it is np hard also
so answer d is 100 prcnt correct.
reason
a probllem is said to be np complete if
a) if it is np hard
b) if it is in np
in question it is given tha it is in np
so 2nd condition is met for being np complete
by option d 1st condition also matches as some problem can be redused to it so it is np hard also
so answer d is 100 prcnt correct.
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A problem in NP is NP-complete ifa)It can be reduced to the 3-SAT problem in polynomial time.b)The 3-SAT problem can be reduced to it in polynomial time.c)It can be reduced to any other problem in NP in polynomial time.d)Some problem in NP can be reduced to it in polynomial time.Correct answer is option 'A'. Can you explain this answer?
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