P ⊆ NP

Turing Machine

Turing Machine

In computational complexity theory, P […] is one of the most fundamental complexity classes. It contains all […] problems which can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. [P-complexity] The complexity class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time. [Turing machine] “So P = NP means that for every problem that has an efficiently verifiable solution, we can find that solution efficiently as well.” (Lance Fortnow) [The Status of the P Versus NP Problem]
C’mon, don’t tell me you know all about the P v.s. NP stuff, including NP-complete, NP-hard, Pseudo-polynomial time, NP-easy, NP-equivalent, and the whole Complexity Zoo.