Which statement correctly describes the relationship between P and NP?

Options

  • A. Every problem in P can also be verified in polynomial time
  • B. Every problem in NP is known to be in P
  • C. P and NP are proven to be different
  • D. More than one of the above
  • E. None of the above

Correct Answer (Detailed Explanation is Below)

A. Every problem in P can also be verified in polynomial time

Detailed Explanation

P contains decision problems that can be solved in polynomial time by a deterministic algorithm. NP contains decision problems whose proposed solutions can be verified in polynomial time. Every problem in P is therefore also in NP, giving the relationship P ⊆ NP. However, whether P equals NP remains an open problem in theoretical computer science. It has not been proven that P = NP or that P ≠ NP. This distinction is fundamental to understanding NP-Complete problems.
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