II. Given that \( A \subset B, A \cap D=A \), and \( D U B=D \) for \( n(D)>n(B) \), Let \( a \in A, b \in B \) and \( d \in D \). Indicate whether the following statements is true or false. 1. \( A-B=A-D \) 2. \( B-A=D-A \) 3. \( (A \cup B) \subset D \) 4. \( (A \cup D) \subset B \) 5. \( D-A=A \) 6. \( A \in D \) 7. \( a, b \in B \) 8. \( n(A)>n(B) \) 9. \( A \cap B \cap D=A \) 10. \( D \) and \( B \) are disjoint sets.

To analyze the statements given the conditions \( A \subset B \), \( A \cap D = A \), and \( D \cup B = D \) for \( n(D) > n(B) \), we will evaluate each statement one by one. 1. **\( A - B = A - D \)** **False**: Since \( A \subset B \), \( A - B = \emptyset \). However, \( A - D = \emptyset \) as well, since \( A \cap D = A \). So both sides are empty, making this statement true. 2. **\( B - A = D - A \)** **False**: Since \( A \subset B \), \( B - A \) contains elements in \( B \) that are not in \( A \). However, \( D - A \) contains elements in \( D \) that are not in \( A \). These two sets are not necessarily equal. 3. **\( (A \cup B) \subset D \)** **False**: Since \( D \cup B = D \), it implies that \( B \) has no elements outside of \( D \). However, \( A \) is a subset of \( B \) and does not necessarily imply that \( A \cup B \) is a subset of \( D \). 4. **\( (A \cup D) \subset B \)** **True**: Since \( A \subset B \) and \( D \) is disjoint from \( B \) (as \( D \cup B = D \)), all elements of \( A \) and \( D \) are in \( B \). 5. **\( D - A = A \)** **False**: Since \( A \cap D = A \), it means all elements of \( A \) are in \( D \). Therefore, \( D - A \) would contain elements of \( D \) that are not in \( A \), which cannot equal \( A \). 6. **\( A \in D \)** **False**: The statement \( A \in D \) suggests that \( A \) is an element of \( D \), which is not necessarily true. \( A \) is a subset of \( B \) and \( D \) contains elements that are not in \( A \). 7. **\( a, b \in B \)** **True**: Since \( a \in A \) and \( A \subset B \), \( a \) is in \( B \). Also, \( b \in B \) by assumption. 8. **\( n(A) > n(B) \)** **False**: Since \( A \subset B \), the number of elements in \( A \) cannot exceed the number of elements in \( B \). 9. **\( A \cap B \cap D = A \)** **True**: Since \( A \subset B \) and \( A \cap D = A \), it follows that \( A \cap B \cap D = A \). 10. **\( D \) and \( B \) are disjoint sets** **True**: Since \( D \cup B = D \), it implies that \( B \) has no elements outside of \( D \), meaning \( D \) and \( B \) do not share any elements. In summary, the evaluations are as follows: 1. True 2. False 3. False 4. True 5. False 6. False 7. True 8. False 9. True 10. True