A pet store surveyed 132 people to gather information about the types of pet they own. 66 people said they own a bird, 85 said they own a cat and 47 said they own both a bird and a cat

This problem involves using the principle of inclusion-exclusion to find out how many people own only a bird, only a cat, or neither.

### Given Information:
- Total number of surveyed people: \( 132 \)
- People who own a bird: \( 66 \)
- People who own a cat: \( 85 \)
- People who own both a bird and a cat: \( 47 \)

### Questions to Answer:
1. **How many people own only a bird?**
2. **How many people own only a cat?**
3. **How many people own either a bird or a cat (or both)?**
4. **How many people do not own either a bird or a cat?**

### Solutions:

1. **Number of people who own only a bird:**

   To find the number of people who own only a bird, subtract the number of people who own both a bird and a cat from the number of people who own a bird:
   \[
   \text{People who own only a bird} = 66 - 47 = 19
   \]

2. **Number of people who own only a cat:**

   Similarly, subtract the number of people who own both a bird and a cat from the number of people who own a cat:
   \[
   \text{People who own only a cat} = 85 - 47 = 38
   \]

3. **Number of people who own either a bird or a cat (or both):**

   Use the principle of inclusion-exclusion to find the number of people who own either a bird or a cat (or both):
   \[
   \text{People who own either or both} = 66 + 85 - 47 = 104
   \]

4. **Number of people who do not own either a bird or a cat:**

   Subtract the number of people who own either a bird or a cat (or both) from the total number of surveyed people:
   \[
   \text{People who do not own either} = 132 - 104 = 28
   \]

### Summary:
- **People who own only a bird:** 19
- **People who own only a cat:** 38
- **People who own either a bird or a cat (or both):** 104
- **People who do not own either:** 28

Would you like further clarification on any part of this solution or have any more questions?

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### Relative Questions:
1. How many people own exactly one pet (either a bird or a cat, but not both)?
2. What percentage of the surveyed people own both a bird and a cat?
3. If 10 more people owned both a bird and a cat, how would the calculations change?
4. How many more people would need to own only a cat to have an equal number of cat-only and bird-only owners?
5. How would the results change if the total number of surveyed people increased to 200?

### Tip:
When solving problems involving sets and overlapping categories, the principle of inclusion-exclusion is a powerful tool for accurately counting elements in various categories.

Explore the results of a pet store survey analyzing pet ownership of birds and cats. Learn how to use the principle of inclusion-exclusion to determine the number of people owning only a bird, only a cat, both, or neither. Discover key insights from 132 survey responses.

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