In a survey of 121 pet owners, 50 said they own a dog, and 48 said they own a cat. 14 said they own both a dog and a cat. How many owned a cat but not a dog?

To solve this, we'll use set theory principles and the inclusion-exclusion formula.

Let:
- \( D \) be the set of people who own a dog.
- \( C \) be the set of people who own a cat.
- \( |D| = 50 \), the number of people who own a dog.
- \( |C| = 48 \), the number of people who own a cat.
- \( |D \cap C| = 14 \), the number of people who own both a dog and a cat.

We want to find the number of people who own a cat but not a dog, which is \( |C \setminus D| \).

Using the formula:
\[
|C \setminus D| = |C| - |D \cap C|
\]
Substitute the values:
\[
|C \setminus D| = 48 - 14 = 34
\]

Thus, **34 people own a cat but not a dog**.

Would you like further details or have any questions? Here are five related questions to expand on this:

1. How many people own a dog but not a cat?
2. How many people own either a dog or a cat but not both?
3. How many people own neither a dog nor a cat?
4. What percentage of the total survey owns a cat?
5. How many people own either a dog or a cat or both?

**Tip**: Understanding Venn diagrams can help visualize overlapping sets, which is useful in solving problems like this.

Solve a set theory problem using the inclusion-exclusion principle. In this survey of 121 pet owners, 50 own a dog, 48 own a cat, and 14 own both. Learn how to calculate how many people own only a cat. Suitable for Grades 6-8.

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