https://file.aiquickdraw.com/mathbot/file/1726458563330rjzupeu5.jpg

The Venn diagram shows two sets, \(A\) and \(B\), with elements distributed across four regions:

- Region I: Elements in set \(A\) only = 29
- Region II: Elements in both set \(A\) and set \(B\) (intersection) = 15
- Region III: Elements in set \(B\) only = 6
- Region IV: Elements outside both sets \(A\) and \(B\) (the universal set but not in \(A\) or \(B\)) = 26

The problem asks how many elements belong to both set \(A\) and set \(B\). This refers to the number of elements in the intersection of \(A\) and \(B\), which is located in Region II of the Venn diagram.

Thus, the number of elements in both \(A\) and \(B\) is:
\[
\boxed{15}
\]

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How would you find the total number of elements in set \(A\)?
2. How would you calculate the total number of elements in set \(B\)?
3. What is the total number of elements in the universal set \(U\)?
4. How would you find the number of elements that are either in set \(A\) or set \(B\)?
5. What is the difference between the union and intersection of two sets?

**Tip:** When working with Venn diagrams, remember that the intersection represents elements common to both sets, while the union covers all elements from both sets.

How many elements belong to set A and set B?

Learn how to use a Venn diagram to find the number of elements in the union of sets A and B. This problem demonstrates key set theory concepts like union, intersection, and the principle of inclusion-exclusion. Suitable for students in Grades 6-8.

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