If `A={1,3,5,7,9},B={2,4,6,8}andC={2,3,5,7,11}`, find `(AnnB)and(AnnC)`. What do you conclude?

Answer

To solve the problem, we need to find the intersection of sets A and B, and then the intersection of sets A and C.

Given:
- \( A = \{1, 3, 5, 7, 9\} \)
- \( B = \{2, 4, 6, 8\} \)
- \( C = \{2, 3, 5, 7, 11\} \)

### Step 1: Find \( A \cap B \)

The intersection \( A \cap B \) consists of elements that are present in both sets A and B.

- Check each element of A:
- 1 is not in B
- 3 is not in B
- 5 is not in B
- 7 is not in B
- 9 is not in B

Since there are no common elements between sets A and B, we conclude:
\[ A \cap B = \emptyset \]

### Step 2: Find \( A \cap C \)

Next, we find the intersection \( A \cap C \) which consists of elements that are present in both sets A and C.

- Check each element of A:
- 1 is not in C
- 3 is in C
- 5 is in C
- 7 is in C
- 9 is not in C

The common elements between sets A and C are:
\[ A \cap C = \{3, 5, 7\} \]

### Conclusion

We have found:
- \( A \cap B = \emptyset \)
- \( A \cap C = \{3, 5, 7\} \)

From this, we can conclude that there are no common elements between sets A and B, while there are some common elements between sets A and C.