For any two sets A and B, B' - A' = ?

Options

A. `A cap B`
B. `A cup B`
C. `A - B`
D. `B - A`

Answer

To solve the question \( B' - A' \), where \( B' \) is the complement of set \( B \) and \( A' \) is the complement of set \( A \), we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Complements**:
- The complement of a set \( A \), denoted \( A' \), consists of all elements not in \( A \).
- Similarly, \( B' \) consists of all elements not in \( B \).

2. **Visualizing the Sets**:
- Imagine a universal set \( U \) that contains all possible elements.
- Set \( A \) is a subset of \( U \) and set \( B \) is another subset of \( U \).

3. **Identifying \( B' \)**:
- \( B' \) includes all elements in \( U \) that are not in \( B \).

4. **Identifying \( A' \)**:
- \( A' \) includes all elements in \( U \) that are not in \( A \).

5. **Finding \( B' - A' \)**:
- The expression \( B' - A' \) means we are taking all elements in \( B' \) and removing those that are in \( A' \).
- This can be interpreted as finding the elements that are in \( B' \) but not in \( A' \).

6. **Understanding the Result**:
- The elements that remain after removing \( A' \) from \( B' \) are those that are in \( B \) but not in \( A \).
- This is equivalent to the set difference \( B - A \).

7. **Conclusion**:
- Therefore, we can conclude that \( B' - A' = B - A \).

### Final Answer:
\[ B' - A' = B - A \]