Final answer:
The P Versus NP Problem is a major unsolved question in computer science that asks if problems that can be verified quickly ('NP') can also be solved quickly ('P'). It is part of the seven Millennium Prize Problems and has profound implications for various fields if solved.Option B is the correct answer.
Step-by-step explanation:
The P Versus NP Problem is a major unsolved problem in computer science that pertains to understanding the relationship between two types of problems: those that are quickly solvable and those for which a solution can be quickly checked. The 'P' in 'P Versus NP' stands for 'Polynomial time,' which refers to problems that can be solved quickly using an algorithm whose running time increases polynomially with the size of the input. In contrast, 'NP' stands for 'Nondeterministic Polynomial time,' which refers to problems for which a proposed solution can be verified quickly, even if finding that solution might take a prohibitively long time.
The P Versus NP Problem asks whether every problem whose solution can be quickly checked ('NP') can also be quickly solved ('P'), which would mean P equals NP. This is a fundamental question because if P were equal to NP, it would mean that many complex problems across various fields could be solved much more efficiently than we currently believe possible. However, to date, no one has been able to prove whether P equals NP or not, making it one of the seven Millennium Prize Problems in mathematics, which are seven of the most challenging problems that remain unsolved.
When approaching any kind of problem, it's important to first identify it clearly. With the P Versus NP Problem, the issue is not only identified but also exemplifies the dichotomy between finding a solution and verifying one. Given its complexity and implications, it is considered one of the most important open questions in computer science and mathematics.