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Check ALL true statements:

a. There is a polynomial-time reduction from 2-SAT to 3-SAT.
b. There is a polynomial-time reduction from 3-SAT to 2-SAT.
c. 2-SAT is in the class P.
d. For any natural number \( k > 1 \), \( k \)-SAT is in the class NP.

Answer :

Final answer:

Reductions from 2-SAT to 3-SAT are possible in polynomial time, 2-SAT is in class P, and k-SAT is in class NP for any k>1; 3-SAT to 2-SAT reduction's existence would imply P=NP.

Explanation:

The question involves understanding concepts from computational complexity theory, specifically polynomial time reduction and complexity classes such as P and NP. The true statements are:

  • There is a polynomial time reduction from 2-SAT to 3-SAT. (True)
  • 2-SAT is in the class P. (True)
  • For any natural number k>1, k-SAT is in the class NP. (True)

There is no known polynomial time reduction from 3-SAT to 2-SAT because 3-SAT is NP-complete, and such a reduction would imply that P=NP, which is a major unsolved question in computer science.

Thanks for taking the time to read Check ALL true statements a There is a polynomial time reduction from 2 SAT to 3 SAT b There is a polynomial time reduction from. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Answer:a, b , c

Explanation: