Let U=` { 5,6,7,8,9 , 10 , 11 , 12 ,13 ,14 , 15 , 16} ` be the universal set and let A = ( 5, 7, 11 , 13 } ,B = { 6,8 , 10 , 12 , 14, 16) and C = ( 5,6,8, 10 , 11, 12 }
be its subsets .
Find
(i) A' (ii) B' (iii) C'

Answer

To find the complements of the sets A, B, and C with respect to the universal set U, we will follow these steps:

### Given:
- Universal Set \( U = \{ 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 \} \)
- Set \( A = \{ 5, 7, 11, 13 \} \)
- Set \( B = \{ 6, 8, 10, 12, 14, 16 \} \)
- Set \( C = \{ 5, 6, 8, 10, 11, 12 \} \)

### Step 1: Find \( A' \) (Complement of A)
1. Identify the elements in the universal set \( U \) that are not in set \( A \).
2. The elements in \( A \) are \( 5, 7, 11, 13 \).
3. Remove these elements from \( U \):
- \( 6 \) is in \( U \) but not in \( A \)
- \( 8 \) is in \( U \) but not in \( A \)
- \( 9 \) is in \( U \) but not in \( A \)
- \( 10 \) is in \( U \) but not in \( A \)
- \( 12 \) is in \( U \) but not in \( A \)
- \( 14 \) is in \( U \) but not in \( A \)
- \( 15 \) is in \( U \) but not in \( A \)
- \( 16 \) is in \( U \) but not in \( A \)

Thus, \( A' = \{ 6, 8, 9, 10, 12, 14, 15, 16 \} \).

### Step 2: Find \( B' \) (Complement of B)
1. Identify the elements in the universal set \( U \) that are not in set \( B \).
2. The elements in \( B \) are \( 6, 8, 10, 12, 14, 16 \).
3. Remove these elements from \( U \):
- \( 5 \) is in \( U \) but not in \( B \)
- \( 7 \) is in \( U \) but not in \( B \)
- \( 9 \) is in \( U \) but not in \( B \)
- \( 11 \) is in \( U \) but not in \( B \)
- \( 13 \) is in \( U \) but not in \( B \)
- \( 15 \) is in \( U \) but not in \( B \)

Thus, \( B' = \{ 5, 7, 9, 11, 13, 15 \} \).

### Step 3: Find \( C' \) (Complement of C)
1. Identify the elements in the universal set \( U \) that are not in set \( C \).
2. The elements in \( C \) are \( 5, 6, 8, 10, 11, 12 \).
3. Remove these elements from \( U \):
- \( 7 \) is in \( U \) but not in \( C \)
- \( 9 \) is in \( U \) but not in \( C \)
- \( 13 \) is in \( U \) but not in \( C \)
- \( 14 \) is in \( U \) but not in \( C \)
- \( 15 \) is in \( U \) but not in \( C \)
- \( 16 \) is in \( U \) but not in \( C \)

Thus, \( C' = \{ 7, 9, 13, 14, 15, 16 \} \).

### Final Answers:
- \( A' = \{ 6, 8, 9, 10, 12, 14, 15, 16 \} \)
- \( B' = \{ 5, 7, 9, 11, 13, 15 \} \)
- \( C' = \{ 7, 9, 13, 14, 15, 16 \} \)