If A and B are two sets satisfying A-B = B - A. then which one of the following is correct?

Options

A. `A=phi`
B. `A cap B = phi`
C. `A=B`
D. None of these

Answer

To solve the problem, we need to analyze the condition given: \( A - B = B - A \).

### Step-by-Step Solution:

1. **Understanding Set Difference**:
The expression \( A - B \) represents the elements that are in set A but not in set B. Similarly, \( B - A \) represents the elements that are in set B but not in set A.

2. **Setting Up the Equation**:
The condition \( A - B = B - A \) implies that the elements unique to A are the same as the elements unique to B.

3. **Analyzing the Implications**:
If \( A - B \) equals \( B - A \), it indicates that the elements that are in A but not in B are exactly the same as the elements that are in B but not in A. This can only happen if both sets A and B have no unique elements.

4. **Considering the Possibilities**:
- If both sets A and B have no elements (i.e., both are empty), then \( A - B = \emptyset \) and \( B - A = \emptyset \), satisfying the condition.
- If A and B have some elements but are not equal, then there will be elements in one set that are not in the other, leading to a contradiction.

5. **Conclusion**:
The only way for \( A - B \) to equal \( B - A \) is if both sets are equal, or both sets are empty. Therefore, we conclude that \( A = B \).

### Final Answer:
The correct option is **C: A = B**.