If `A - B =phi phi and B-A = phi ` then what can we conclude ?

Explanation

To solve the problem, we need to analyze the given conditions step by step.

### Given:
1. \( A - B = \phi \)
2. \( B - A = \phi \)

### Step 1: Understand the meaning of the conditions
- The expression \( A - B \) represents the elements that are in set \( A \) but not in set \( B \). If \( A - B = \phi \), it means there are no elements in \( A \) that are not in \( B \). Thus, every element of \( A \) must be in \( B \).

- Similarly, \( B - A = \phi \) means there are no elements in \( B \) that are not in \( A \). Thus, every element of \( B \) must be in \( A \).

### Conclusion from Step 1:
From these two conditions, we can conclude that:
- Every element of \( A \) is in \( B \) (i.e., \( A \subseteq B \)).
- Every element of \( B \) is in \( A \) (i.e., \( B \subseteq A \)).

### Step 2: Combine the conclusions
Since \( A \subseteq B \) and \( B \subseteq A \), we can conclude that:
- \( A = B \)

### Final Conclusion:
Thus, from the given conditions \( A - B = \phi \) and \( B - A = \phi \), we conclude that:
- \( A = B \)