If A and B are two sets ,then `(A-B)uu(B-A)uu(AnnB)` equals

Options

A. `AuuB`
B. `AnnB`
C. A
D. B'

Answer

To solve the problem, we need to simplify the expression \((A - B) \cup (B - A) \cup (A \cap B)\).

### Step-by-Step Solution:

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

2. **Understanding Set Intersection**:
- The expression \(A \cap B\) represents the elements that are common to both sets \(A\) and \(B\).

3. **Combining the Sets**:
- We need to find the union of these three sets: \((A - B) \cup (B - A) \cup (A \cap B)\).
- The union of sets means we take all unique elements from each of the sets involved.

4. **Visualizing the Sets**:
- If we visualize sets \(A\) and \(B\), we can see that:
- \(A - B\) includes elements only in \(A\).
- \(B - A\) includes elements only in \(B\).
- \(A \cap B\) includes elements that are in both \(A\) and \(B\).

5. **Resulting Set**:
- When we take the union of \((A - B)\), \((B - A)\), and \((A \cap B)\), we effectively include:
- All elements from \(A\) (both unique and common).
- All elements from \(B\) (both unique and common).
- Therefore, the union of these three sets is simply the union of sets \(A\) and \(B\), which is denoted as \(A \cup B\).

6. **Final Answer**:
- Thus, we conclude that \((A - B) \cup (B - A) \cup (A \cap B) = A \cup B\).

### Conclusion:
The expression \((A - B) \cup (B - A) \cup (A \cap B)\) equals \(A \cup B\).