Let U= { 1,2,3,4,5,6,7,8,9,10 } be the universal set and let A = {2,3,4,5,6} and B = { 3,5,7,8} be its subsets .
Find ` A' nn B ' `

Answer

To solve the problem of finding \( A' \cap B' \) given the universal set \( U \), set \( A \), and set \( B \), we will follow these steps:

### Step 1: Identify the Universal Set and the Sets A and B
- Universal Set \( U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \} \)
- Set \( A = \{ 2, 3, 4, 5, 6 \} \)
- Set \( B = \{ 3, 5, 7, 8 \} \)

### 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 \( A \).
- \( A' = U - A \)
- \( A' = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \} - \{ 2, 3, 4, 5, 6 \} \)
- \( A' = \{ 1, 7, 8, 9, 10 \} \)

### Step 3: Find the Complement of Set B
The complement of set \( B \) (denoted as \( B' \)) consists of all the elements in the universal set \( U \) that are not in \( B \).
- \( B' = U - B \)
- \( B' = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \} - \{ 3, 5, 7, 8 \} \)
- \( B' = \{ 1, 2, 4, 6, 9, 10 \} \)

### Step 4: Find the Intersection of A' and B'
Now we need to find the intersection of \( A' \) and \( B' \) (denoted as \( A' \cap B' \)), which consists of all elements that are present in both \( A' \) and \( B' \).
- \( A' = \{ 1, 7, 8, 9, 10 \} \)
- \( B' = \{ 1, 2, 4, 6, 9, 10 \} \)
- The common elements in both sets are \( \{ 1, 9, 10 \} \).

### Final Answer
Thus, \( A' \cap B' = \{ 1, 9, 10 \} \).

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