Final answer:
The statement A intersects (B union C) = C is not correct unless A and C are identical sets. A and B being subsets of each other implies A = B.
Step-by-step explanation:
If A is a subset of B and B is a subset of A, it means A = B. Both sets contain exactly the same elements. Therefore, A intersecting (B union C) simplifies to A intersecting C since A and B are essentially the same set. Now, we address the original statement that A intersects (B union C) = C.
If A and C are mutually exclusive, which means they have no elements in common, then A intersecting C is indeed the empty set, not C. If A and C do have elements in common, then A intersects (B union C) would be the elements they have in common, which could be a subset of C but not necessarily C itself.
The original statement is not correct unless A and C are exactly the same set, but that wasn't provided in the initial conditions. Examples showing different possibilities of intersection and union with respect to mutually exclusive sets, dependency, and independence can further clarify this concept.