Consider two decision problems 𝑄1,𝑄2 such that 𝑄1 reduces in polynomial…

GATE Β· 2015 Β· CS Β· Set 2 Β· Computer Science & IT

Consider two decision problems 𝑄1,𝑄2 such that 𝑄1 reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to 𝑄2. Then which one of the following is consistent with the above statement?

  1. A.

    𝑄1 is in NP, 𝑄2 is NP hard.

  2. B.

    𝑄2 is in NP, 𝑄1 is NP hard.

  3. C.

    Both 𝑄1 and 𝑄2 are in NP .

  4. D.

    Both 𝑄1 and 𝑄2 are NP hard.

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