GATE | GATE-CS-2003 | Question 12

Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions ?
(A) Π is NP-hard but not NP-complete
(B) Π is in NP, but is not NP-complete
(C) Π is NP-complete
(D) Π is neither NP-hard, nor in NP


Answer: (C)

Explanation: Since polynomial time reduction from the 3-SAT problem to Π is possible, it is NP hard.

Since polynomial time reduction from Π to 3-SAT is possible, it is NP-Complete.

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