U= {12,13,14,15,16,17,18,19,20,21} A={15,16,1718} B={12,14,16,18,20}. A n B'=


We are tasked with finding \( A \cap B' \), where:

- \( U = \{12, 13, 14, 15, 16, 17, 18, 19, 20, 21\} \) is the universal set,
- \( A = \{15, 16, 17, 18\} \),
- \( B = \{12, 14, 16, 18, 20\} \).

### Steps to solve:

1. **Find \( B' \) (the complement of B with respect to U):**

   The complement of \( B \) is the set of elements in \( U \) that are not in \( B \):
   \[
   B' = U - B = \{13, 15, 17, 19, 21\}.
   \]

2. **Find \( A \cap B' \) (the intersection of A and B'):**

   The intersection of two sets contains the elements that are in both sets. We now find the common elements between \( A \) and \( B' \):
   \[
   A = \{15, 16, 17, 18\}, \quad B' = \{13, 15, 17, 19, 21\}.
   \]

   The common elements are \( \{15, 17\} \).

### Final Answer:
\[
A \cap B' = \{15, 17\}.
\]

Would you like more details or have any questions?

Here are some related questions to think about:
1. What would \( A \cup B \) (the union of A and B) look like?
2. How do you find the complement of a set?
3. What would happen if we calculated \( B \cap A' \)?
4. What is the difference between \( A - B \) and \( B - A \)?
5. How do we use Venn diagrams to visualize set operations?

**Tip:** Always double-check the universal set when finding complements to avoid missing elements.

The query submitted by the user: U={12,13,14,15,16,17,18,19,20,21}, A={15,16,17,18}, B={12,14,16,18,20}. A n B' = ?

Solve the problem of finding A ∩ B', where U = {12, 13, 14, 15, 16, 17, 18, 19, 20, 21}, A = {15, 16, 17, 18}, and B = {12, 14, 16, 18, 20}. The solution covers key concepts in set theory, including intersections and complements, suitable for students in Grades 8-10.

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