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Which of the following is TRUE ?

  • A.\(P = NP\)
  • B.\(P \neq NP\)
  • C.\(P \subset NP\)
  • D.\(P \subseteq NP\)

Answer: D

The true statement is \(P \subseteq NP\).

Every problem solvable in polynomial time can also be verified in polynomial time (just solve it), so P is contained in NP. That containment is proved.

Whether the containment is proper is the open P versus NP question. So \(P = NP\), \(P \neq NP\) and the proper subset \(P \subset NP\) are all unproven, and only \(P \subseteq NP\) is known to be true.

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