Find the intersection of the sets
`A={1,2,3,4,5,6}`, `B={2,4,5}`, `C={2,6}` and show that `(AnnB)nnC=Ann(BnnC)`.

Answer

To solve the problem, we need to find the intersection of the sets \( A \), \( B \), and \( C \), and then show that \( (A \cap B) \cap C = A \cap (B \cap C) \).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Let \( A = \{1, 2, 3, 4, 5, 6\} \)
- Let \( B = \{2, 4, 5\} \)
- Let \( C = \{2, 6\} \)

2. **Find \( A \cap B \)**:
- The intersection \( A \cap B \) consists of elements that are common to both sets \( A \) and \( B \).
- Common elements: \( 2 \) and \( 4 \) and \( 5 \).
- Thus, \( A \cap B = \{2, 4, 5\} \).

3. **Find \( (A \cap B) \cap C \)**:
- Now, we need to find the intersection of \( A \cap B \) with \( C \).
- We have \( A \cap B = \{2, 4, 5\} \) and \( C = \{2, 6\} \).
- The common element is \( 2 \).
- Therefore, \( (A \cap B) \cap C = \{2\} \).

4. **Find \( B \cap C \)**:
- Next, we find the intersection of \( B \) and \( C \).
- We have \( B = \{2, 4, 5\} \) and \( C = \{2, 6\} \).
- The common element is \( 2 \).
- Thus, \( B \cap C = \{2\} \).

5. **Find \( A \cap (B \cap C) \)**:
- Now, we need to find the intersection of \( A \) with \( B \cap C \).
- We have \( A = \{1, 2, 3, 4, 5, 6\} \) and \( B \cap C = \{2\} \).
- The common element is \( 2 \).
- Therefore, \( A \cap (B \cap C) = \{2\} \).

6. **Conclusion**:
- We have found that:
- \( (A \cap B) \cap C = \{2\} \)
- \( A \cap (B \cap C) = \{2\} \)
- Thus, we can conclude that \( (A \cap B) \cap C = A \cap (B \cap C) \).

### Final Result:
\[ (A \cap B) \cap C = A \cap (B \cap C) = \{2\} \]