If U = {1,2,3,4,5,6,7,8,9} and A = {1,2,3,4} , then `(A^(c))^(c)` = ……….. .

Answer

To solve the problem, we need to find the value of \( (A^c)^c \), where \( A^c \) is the complement of set \( A \) with respect to the universal set \( U \).

### Step-by-Step Solution:

1. **Identify the Universal Set \( U \) and Set \( A \)**:
- Given \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- Given \( A = \{1, 2, 3, 4\} \)

2. **Find the Complement of Set \( A \)**:
- The complement of \( A \) (denoted as \( A^c \)) consists of all elements in \( U \) that are not in \( A \).
- Elements in \( A \): \( 1, 2, 3, 4 \)
- Elements in \( U \) not in \( A \): \( 5, 6, 7, 8, 9 \)
- Therefore, \( A^c = \{5, 6, 7, 8, 9\} \)

3. **Find the Complement of \( A^c \)**:
- Now, we need to find \( (A^c)^c \), which is the complement of \( A^c \).
- This consists of all elements in \( U \) that are not in \( A^c \).
- Elements in \( A^c \): \( 5, 6, 7, 8, 9 \)
- Elements in \( U \) not in \( A^c \): \( 1, 2, 3, 4 \)
- Therefore, \( (A^c)^c = \{1, 2, 3, 4\} \)

4. **Conclusion**:
- We find that \( (A^c)^c = A \).
- Thus, the final answer is \( (A^c)^c = \{1, 2, 3, 4\} \).

### Final Answer:
\[ (A^c)^c = \{1, 2, 3, 4\} \]