If the sets A and B are given by `A = {1, 2, 3, 4} B = {2, 4, 6, 8, 10}` and the universal set `U = {1,2,3,4,5,6,7,8,9,10}` then

Options

A. `(AuuB)' = {5,7,9}`
B. `(AnnB)' = {1,3,5,6,7}`
C. `(AnnB)' = {1,3,5,6,7,8,9,10}`
D. 1 & 3 both are correct

Explanation

To solve the problem, we need to find the union and intersection of the sets A and B, and then determine their complements with respect to the universal set U.

### Step-by-Step Solution:

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

2. **Find A Union B (A ∪ B):**
- A ∪ B includes all elements that are in A, in B, or in both.
- A ∪ B = {1, 2, 3, 4} ∪ {2, 4, 6, 8, 10} = {1, 2, 3, 4, 6, 8, 10}

3. **Find the Complement of A Union B (A ∪ B)' with respect to U:**
- The complement of A ∪ B consists of elements in U that are not in A ∪ B.
- A ∪ B = {1, 2, 3, 4, 6, 8, 10}
- U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- A ∪ B' = U - (A ∪ B) = {5, 7, 9}

4. **Find A Intersection B (A ∩ B):**
- A ∩ B includes all elements that are in both A and B.
- A ∩ B = {2, 4}

5. **Find the Complement of A Intersection B (A ∩ B)' with respect to U:**
- The complement of A ∩ B consists of elements in U that are not in A ∩ B.
- A ∩ B = {2, 4}
- A ∩ B' = U - (A ∩ B) = {1, 3, 5, 6, 7, 8, 9, 10}

### Final Results:
- A ∪ B' = {5, 7, 9}
- A ∩ B' = {1, 3, 5, 6, 7, 8, 9, 10}

### Conclusion:
Based on the results, we can determine which options are correct based on the provided information.