Question

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 1

Answer:a, b , c

Step-by-step explanation:

Answer 2

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.

Step-by-step 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.