Consider a general set, A, which is a subset of a general set, Ω. Suppose also that B is the complement of A, i.e. B=Ac=Ω∖A.Next let C be a subset of A (i.e. C⊆A) and D be a subset of B (i.e. D⊆B).Tick the most appropriate answer:D⊆BB∖D=BA∖C=AB∪C=BA∖B=∅A∖C=CA∪D=∅

The given text is a set of mathematical statements related to set theory. Here are the answers:

1. D⊆B: This is true. By definition, D is a subset of B.

2. B∖D=B: This is false. The set difference B\D would be the elements in B that are not in D. If D has at least one element that is also in B, then B\D would not be equal to B.

3. A∖C=A: This is false. The set difference A\C would be the elements in A that are not in C. If C has at least one element that is also in A, then A\C would not be equal to A.

4. B∪C=B: This is false. The union of B and C, B∪C, would include all elements that are in B or C or both. Since C is a subset of A and A and B are disjoint sets (since B is the complement of A), B∪C would not be equal to B.

5. A∖B=∅: This is true. Since B is the complement of A, there are no elements in A that are also in B. Therefore, the set difference A\B would be an empty set.

6. A∖C=C: This is false. The set difference A\C would be the elements in A that are not in C. It would not be equal to C.

7. A∪D=∅: This is false. The union of A and D, A∪D, would include all elements that are in A or D or both. Since A and D are subsets of Ω, their union would not be an empty set.