Which of the following statements maybe false for a decision problem X ∈ NP?

Explanation

By the definition of the class NP, every problem X ∈ NP can be solved (verified) in nondeterministic polynomial time, so that statement is always true. Since NP ⊆ EXPTIME, X can always be solved in deterministic exponential time, and since NP ⊆ PSPACE, X can always be solved in polynomial space as well, so both of those are always true too. Whether every problem in NP can also be solved in deterministic polynomial time is exactly the open P versus NP question, so it is not guaranteed to be true for an arbitrary X ∈ NP (it would be false for some problems if P ≠ NP). The statement that may be false is therefore X can be solved in deterministic polynomial time.