Venn Diagram Worksheets - Free Printable

Let's go through each problem step by step using the Venn diagrams provided and explain how to arrive at the correct answers.

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Problem 1:

Diagram:
- Desktop only: 4
- Both desktop and laptop: 7
- Laptop only: 9

Question: How many students did not own both a desktop and a laptop computer?

Solution:
We are asked for the number of students who did not own both types. That means we want all students except those in the intersection (the overlapping part).

Total students = Desktop only + Both + Laptop only
= 4 + 7 + 9 = 20

Students who owned both = 7

So, students who did not own both = Total – Both = 20 – 7 = 13

✔ Answer: 13

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Problem 2:

Diagram:
- Red only: 6
- Both red and thorns: 6
- Thorns only: 8

Question: How many flowers were red with thorns?

Solution:
"Red with thorns" means the intersection of red and thorns → that’s the overlapping region.

That value is 6

✔ Answer: 6

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Problem 3:

Diagram:
- Soccer only: 14
- Both soccer and baseball: 9
- Baseball only: 3

Question: How many people watched soccer?

Solution:
People who watched soccer = Soccer only + Both
= 14 + 9 = 23

✔ Answer: 23

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Problem 4:

Diagram:
- PS4 only: 9
- Both PS4 and Xbox: 9
- Xbox only: 8

Question: How many people owned both a PS4 and an Xbox?

Solution:
The overlap (intersection) is the number of people who own both → that’s 9

✔ Answer: 9

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Problem 5:

Diagram:
- Brother only: 12
- Both brother and sister: 13
- Sister only: 11

Question: How many students did not have both a brother and a sister?

Solution:
We want students who do not have both, so exclude the intersection.

Total students = 12 + 13 + 11 = 36
Students with both = 13
So, students who did not have both = 36 – 13 = 23

✔ Answer: 23

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Problem 6:

Diagram:
- Dog only: 19
- Both dog and cat: 6
- Cat only: 19

Question: How many people had a cat?

Solution:
People who had a cat = Cat only + Both
= 19 + 6 = 25

✔ Answer: 25

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✔ Final Answers:

1. 13
2. 6
3. 23
4. 9
5. 23
6. 25

These match the answer key provided.

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Summary of Key Concepts:

- The overlap in a Venn diagram represents elements that belong to both sets.
- To find “how many are in either set,” add all parts.
- To find “how many are not in both,” subtract the intersection from the total.
- Always read the question carefully — “both” means intersection; “either” means union.

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