Let U= {1, 2, 3, 4, 5, 6, 7, 8,9}, A={1, 2, 3, 4}, B = {2, 4, 6, 8) and C={3, 4, 5, 6}. Find
`(A')'`

Answer

To solve the problem of finding \( (A')' \), where \( A' \) is the complement of set \( A \) and \( (A')' \) is the complement of the complement of \( A \), we can follow these steps:

### Step 1: Identify the Universal Set and Set A
The universal set \( U \) is given as:
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \]

Set \( A \) is given as:
\[ A = \{1, 2, 3, 4\} \]

### Step 2: Find the Complement of Set A
The complement of set \( A \), denoted as \( A' \), consists of all the elements in the universal set \( U \) that are not in \( A \).

To find \( A' \):
\[ A' = U - A \]
\[ A' = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} - \{1, 2, 3, 4\} \]
\[ A' = \{5, 6, 7, 8, 9\} \]

### Step 3: Find the Complement of the Complement of Set A
Now we need to find \( (A')' \), which is the complement of \( A' \).

To find \( (A')' \):
\[ (A')' = U - A' \]
\[ (A')' = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} - \{5, 6, 7, 8, 9\} \]
\[ (A')' = \{1, 2, 3, 4\} \]

### Conclusion
Thus, the result of \( (A')' \) is:
\[ (A')' = \{1, 2, 3, 4\} \]