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Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.
(i) AB (A is reducible to B)
(ii) C D
(iii) B D
Find the correct statement from the following.
- a)if A is decidable, B is decidable
- b)if D is undecidable, B is undecidable
- c)if C is decidable, B is decidable
- d)if A is undecidable, B is undecidable
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let A, B, C and D are problems. Consider the following polynomial red...
A ≤ B
C ≤ D
B ≤ D
A. A is decidable ⇒ B need not be decidable.
B. D is undecidable ⇒ B need not be undecidable.
C. C is decidable ⇒ D need not be decidable.
D. A is undecidable ⇒ B is undecidable.
Most Upvoted Answer
Let A, B, C and D are problems. Consider the following polynomial red...
Explanation:
To determine the correct statement, we need to analyze the given polynomial reductions and their relationship with the decidability of the problems.
Reduction (i): AB (A is reducible to B)
This reduction implies that problem A can be solved using problem B. If A is decidable, it means that there exists an algorithm that can decide whether an instance of problem A is a "yes" instance or a "no" instance. Since A can be reduced to B, we can use the algorithm for B to solve A. Therefore, if A is decidable, it implies that B is also decidable.
Reduction (ii): C D
This reduction does not provide any information about the decidability of problem B. It only states that problem C can be reduced to problem D, but it does not give any insights into the relationship between problem B and problem C.
Reduction (iii): B D
This reduction implies that problem D can be solved using problem B. If D is undecidable, it means that there is no algorithm that can decide whether an instance of problem D is a "yes" instance or a "no" instance. However, since D can be reduced to B, we can use the algorithm for B to solve D. Therefore, if D is undecidable, it implies that B is also undecidable.
Conclusion:
Based on the given reductions, the correct statement is option 'D' - if A is undecidable, B is undecidable. This is because if A is undecidable, it means that there is no algorithm that can decide whether an instance of problem A is a "yes" instance or a "no" instance. If A can be reduced to B, then we can use the algorithm for B to solve A. However, since A is undecidable, it implies that B is also undecidable.
Therefore, option 'D' is the correct statement based on the given reductions.
To determine the correct statement, we need to analyze the given polynomial reductions and their relationship with the decidability of the problems.
Reduction (i): AB (A is reducible to B)
This reduction implies that problem A can be solved using problem B. If A is decidable, it means that there exists an algorithm that can decide whether an instance of problem A is a "yes" instance or a "no" instance. Since A can be reduced to B, we can use the algorithm for B to solve A. Therefore, if A is decidable, it implies that B is also decidable.
Reduction (ii): C D
This reduction does not provide any information about the decidability of problem B. It only states that problem C can be reduced to problem D, but it does not give any insights into the relationship between problem B and problem C.
Reduction (iii): B D
This reduction implies that problem D can be solved using problem B. If D is undecidable, it means that there is no algorithm that can decide whether an instance of problem D is a "yes" instance or a "no" instance. However, since D can be reduced to B, we can use the algorithm for B to solve D. Therefore, if D is undecidable, it implies that B is also undecidable.
Conclusion:
Based on the given reductions, the correct statement is option 'D' - if A is undecidable, B is undecidable. This is because if A is undecidable, it means that there is no algorithm that can decide whether an instance of problem A is a "yes" instance or a "no" instance. If A can be reduced to B, then we can use the algorithm for B to solve A. However, since A is undecidable, it implies that B is also undecidable.
Therefore, option 'D' is the correct statement based on the given reductions.
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Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer?
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Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer?.
Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.a)if A is decidable, B is decidableb)if D is undecidable, B is undecidablec)if C is decidable, B is decidabled)if A is undecidable, B is undecidableCorrect answer is option 'D'. Can you explain this answer?.
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