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The statement that all P problems fall under the category of NP problems is indeed true. To understand this, it's essential to clarify the definitions of P and NP.

P refers to the class of problems that can be solved in polynomial time by a deterministic Turing machine. Essentially, these are problems for which there exists an efficient algorithm that can find the solution in a time that grows polynomially with the input size.

NP, on the other hand, encompasses problems for which a proposed solution can be verified in polynomial time. If you can quickly check, given an answer, whether it is correct or not, then the problem belongs to NP.

Since any problem that can be solved in polynomial time can also be verified in polynomial time (you can simply compute the solution and check it against the input), all problems in P can be thought of as falling into NP as well. Therefore, every P problem is also an NP problem.

This relationship is foundational in computational complexity theory and underscores a significant aspect of how these classes are defined. Understanding this relationship is crucial for deeper insights into algorithm efficiency and problem-solving capabilities in computer science.