Let X = {1,2,3, 4,5, 6,7, 8, 9,10} be the universal set and A ={2,4, 6}, B ={1,3,5}, then `A^cnnB^c` is equal to:

Options

A. {2,4,5, 6, 8, 9,10}
B. {1,3,5,7, 8, 9,10}
C. X
D. {7,8,9,10}

Answer

To solve the problem, we need to find \( A^c \cap B^c \) where \( A \) and \( B \) are subsets of the universal set \( X \).

### Step-by-Step Solution:

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

2. **Find the Complement of Set A (\( A^c \)):**
- The complement of \( A \) is the set of elements in \( X \) that are not in \( A \).
- \( A^c = X - A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} - \{2, 4, 6\} \)
- Therefore, \( A^c = \{1, 3, 5, 7, 8, 9, 10\} \)

3. **Find the Complement of Set B (\( B^c \)):**
- The complement of \( B \) is the set of elements in \( X \) that are not in \( B \).
- \( B^c = X - B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} - \{1, 3, 5\} \)
- Therefore, \( B^c = \{2, 4, 6, 7, 8, 9, 10\} \)

4. **Find the Intersection of \( A^c \) and \( B^c \) (\( A^c \cap B^c \)):**
- The intersection is the set of elements that are common to both \( A^c \) and \( B^c \).
- \( A^c = \{1, 3, 5, 7, 8, 9, 10\} \)
- \( B^c = \{2, 4, 6, 7, 8, 9, 10\} \)
- The common elements are \( \{7, 8, 9, 10\} \).

5. **Final Result:**
- Therefore, \( A^c \cap B^c = \{7, 8, 9, 10\} \).

### Conclusion:
The final answer is \( A^c \cap B^c = \{7, 8, 9, 10\} \).