Venn Diagram Worksheets | Dynamically Created Venn Diagram Worksheets - Free Printable

To solve the problems based on the Venn diagram, let's carefully analyze each question step by step. The Venn diagram shows three sets: Skiing, Volleyball, and Soccer. Here are the numbers in each section:

- Only Skiing: 7
- Skiing and Volleyball but not Soccer: 14
- Only Volleyball: 12
- Volleyball and Soccer but not Skiing: 6
- Only Soccer: 19
- Skiing and Soccer but not Volleyball: 9
- All three activities (Skiing, Volleyball, and Soccer): 15

Total Number of Students:

The total number of students can be calculated by summing all the sections of the Venn diagram:
\[
7 + 14 + 12 + 6 + 19 + 9 + 15 = 82
\]

Solutions to Each Question:

1. How many students do not like either Skiing or Volleyball?
- These students are only in the Soccer set and not in Skiing or Volleyball.
- Number: 19
\[
\boxed{19}
\]

2. How many students like Volleyball or Soccer?
- This includes students who like Volleyball, Soccer, or both.
- Sum of Volleyball, Soccer, and their intersection:
\[
12 + 6 + 15 + 19 = 52
\]
\[
\boxed{52}
\]

3. How many students like both Skiing and Soccer but not Volleyball?
- This is the number in the intersection of Skiing and Soccer but not Volleyball.
- Number: 9
\[
\boxed{9}
\]

4. How many students only like Skiing?
- This is the number in the Skiing set but not in Volleyball or Soccer.
- Number: 7
\[
\boxed{7}
\]

5. How many students do not like either Volleyball or Soccer?
- These students are only in the Skiing set and not in Volleyball or Soccer.
- Number: 7
\[
\boxed{7}
\]

6. How many students like Skiing or Soccer but not Volleyball?
- This includes students who like Skiing, Soccer, or both but not Volleyball.
- Sum of Skiing only, Soccer only, and Skiing and Soccer but not Volleyball:
\[
7 + 19 + 9 = 35
\]
\[
\boxed{35}
\]

7. How many students like Volleyball or Soccer but not Skiing?
- This includes students who like Volleyball, Soccer, or both but not Skiing.
- Sum of Volleyball only, Soccer only, and Volleyball and Soccer but not Skiing:
\[
12 + 19 + 6 = 37
\]
\[
\boxed{37}
\]

8. How many students like Skiing or Soccer?
- This includes students who like Skiing, Soccer, or both.
- Sum of Skiing, Soccer, and their intersection:
\[
7 + 9 + 15 + 19 = 50
\]
\[
\boxed{50}
\]

9. How many students like both Skiing and Soccer?
- This includes students who like both Skiing and Soccer, whether they also like Volleyball or not.
- Sum of Skiing and Soccer but not Volleyball, and all three activities:
\[
9 + 15 = 24
\]
\[
\boxed{24}
\]

10. How many students do not like both Skiing and Volleyball?
- These students are either only in Soccer or do not like any of the three activities.
- Since there are no students outside all three circles, we only consider those in Soccer but not in Skiing or Volleyball.
- Number: 19
\[
\boxed{19}
\]

Final Answers:

1. \(\boxed{19}\)
2. \(\boxed{52}\)
3. \(\boxed{9}\)
4. \(\boxed{7}\)
5. \(\boxed{7}\)
6. \(\boxed{35}\)
7. \(\boxed{37}\)
8. \(\boxed{50}\)
9. \(\boxed{24}\)
10. \(\boxed{19}\)