Venn Diagrams (3 Sets) Worksheets. | Worsheets library - Free Printable

Let's solve the Venn diagram problem step by step.

Understanding the Venn Diagram:

The diagram has three overlapping circles representing:
- Math Club
- Arts Club
- Music Club

Each section shows the number of students in specific combinations of clubs.

Here’s how we interpret the numbers:

- Only Math Club: 22
- Only Arts Club: 15
- Only Music Club: 7
- Math and Arts (but not Music): 8
- Math and Music (but not Arts): 6
- Arts and Music (but not Math): 5
- All three clubs (Math, Arts, Music): 12
- None of the clubs: 18

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Now, answer each question:

#### 1. How many students joined only the math club?
This is the part of the Math circle that does not overlap with any other club.
→ 22

✔ Answer: 22

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#### 2. How many students joined the arts club?
This includes all students in the Arts Club circle:
- Only Arts: 15
- Arts and Math (not Music): 8
- Arts and Music (not Math): 5
- All three: 12

Add them up:
15 + 8 + 5 + 12 = 40

✔ Answer: 40

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#### 3. How many students joined a club but did not join the math or arts clubs?
This means they joined only the music club, since it's the only club left.
→ Only Music Club: 7

✔ Answer: 7

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#### 4. How many students joined both the arts club and the music club?
This includes:
- Arts and Music, but not Math: 5
- All three clubs: 12

So total = 5 + 12 = 17

✔ Answer: 17

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#### 5. How many students did not join any clubs?
This is the number outside all circles:
→ 18

✔ Answer: 18

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#### 6. How many students joined all the three clubs?
This is the center where all three circles overlap:
→ 12

✔ Answer: 12

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✔ Final Answers:

1. 22
2. 40
3. 7
4. 17
5. 18
6. 12

Let me know if you'd like a visual explanation or help with similar problems!