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Assuming P ≠ NP, which of the following is TRUE?

Assuming P ≠ NP, which of the following is TRUE? Correct Answer NP-complete ∩ P = Φ

The correct answer is option 2

CONCEPT:

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From Diagram: NP-complete ⋂ P = ϕ

NP-complete problems:

They are those for which no polynomial-time algorithm exists. We can say a problem is NP-complete if it is NP and belongs to NP-hard.

NP problems:

A problem is a member of the NP class if there exists a non-deterministic machine that can solve it in polynomial time.

NP-Hard:

A problem is called NP-hard if all the NP class problems are polynomial-time reducible to that and as hard as any problem of NP class

EXPLANATION:

  • Every problem in P is also in NP
  • Given that P ≠ NP, this means there exists a problem that is in NP but not in P

So the option NP-complete ∩ P = Φ is correct

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