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The relationship between NP-Complete and NP-Hard problems is foundational in computational theory. NP-Complete problems are a subset of NP problems that are both in NP and NP-Hard. This means that if a polynomial-time solution exists for any NP-Complete problem, it implies that every problem in NP can also be solved in polynomial time, establishing a crucial link between the two classes.

Every NP-Complete problem is indeed NP-Hard because NP-Hard represents the class of problems that are at least as hard as the hardest problems in NP. Therefore, solving any NP-Complete problem in polynomial time would allow us to derive solutions to all NP problems, confirming the NP-Complete problems' status as NP-Hard.

NP-Hard problems may not themselves be in NP; they might be more general or even less structured than NP problems. Consequently, while all NP-Complete problems fall under the umbrella of NP-Hard, it does not reciprocate—that is, not all NP-Hard problems are NP-Complete. This differentiates the two categories and underscores why the correct answer accurately represents their relationship.

The other statements do not align with the definitions provided within computational complexity theory, reinforcing the clear hierarchy and relationships between these problem classes.