https://file.aiquickdraw.com/mathbot/file/1725695677036wcf0rojk.jpg

Let's analyze the Venn diagram in the image. The sets \(A\), \(B\), and \(C\) represent students who play tennis, basketball, and another sport (possibly soccer), respectively. The different regions represent combinations of students who participate in multiple activities.

### The information provided:
- \( A \): Tennis players
- \( B \): Basketball players
- \( C \): Players in the third sport

The diagram shows various numbers in the different overlapping and non-overlapping regions:

- The number of students who play only tennis is 9 (as mentioned).
- The number of students who play basketball is 22 (as mentioned).
- The number of students who are in the intersection of \( A \cap (B \cup C) \) is 11 (as mentioned).

### Let’s verify:
Looking at the diagram, the region associated with the intersection of \( A \cap (B \cup C) \) includes:
- The regions where students play both tennis and basketball (2), both tennis and the third sport (3), and all three sports (6).

So, \( 2 + 3 + 6 = 11 \), which matches the given answer.

Would you like to explore these intersections further or focus on other parts of this problem?

---

Here are 5 related questions you could explore:
1. How many students only play basketball?
2. How many students play all three sports?
3. What is the total number of students represented in the diagram?
4. How many students play at least one sport?
5. How many students play only one sport?

**Tip:** When working with Venn diagrams, always ensure that you carefully interpret the overlaps and unique regions for accurate counting.

Based on the Venn diagram, determine the following values:
a) The number of students who play only tennis.
b) The number of students who play basketball.
c) The number of students in A ∩ (B ∪ C).

Analyze a Venn diagram with sets representing students who play different sports. Learn how to calculate the number of students who play only tennis, those who play basketball, and those in the intersection of sets. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation