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This problem is asking to verify if the provided data is consistent, based on survey responses about people's preferences for three beverages: sake (日本酒), beer (ビール), and whiskey (ウイスキー). The data includes:

- 45 people like sake.
- 85 people like beer.
- 60 people like whiskey.
- 30 people like only sake and beer.
- 25 people like only sake and whiskey.
- 55 people like only beer and whiskey.
- 12 people like all three.

The total number of people surveyed is 100.

### Steps to solve the problem:

1. **Label the sets**:
   Let:
   - \( A \) be the set of people who like sake.
   - \( B \) be the set of people who like beer.
   - \( C \) be the set of people who like whiskey.

   We're given:
   - \( |A| = 45 \)
   - \( |B| = 85 \)
   - \( |C| = 60 \)
   - \( |A \cap B| - |A \cap B \cap C| = 30 \) (only sake and beer)
   - \( |A \cap C| - |A \cap B \cap C| = 25 \) (only sake and whiskey)
   - \( |B \cap C| - |A \cap B \cap C| = 55 \) (only beer and whiskey)
   - \( |A \cap B \cap C| = 12 \) (all three)

2. **Use the inclusion-exclusion principle**:
   To verify if the data is consistent, we can calculate the total number of people based on the intersections and check if it equals 100.

   Let's calculate:

   \[
   \text{Total} = |A| + |B| + |C| - (|A \cap B| + |A \cap C| + |B \cap C|) + |A \cap B \cap C|
   \]

3. **Substitute values** and check:
   Now, I will calculate this step-by-step to verify consistency.The calculated total based on the provided data is 80, which does not match the total of 100 people who were surveyed. Therefore, the data given is inconsistent, and it cannot be trusted as it currently stands.

Would you like more details on the process or a breakdown of specific steps? Here are some related questions to explore further:

1. How is the inclusion-exclusion principle used in set theory problems?
2. Can we adjust the numbers to make the data consistent?
3. What are common errors when solving problems involving multiple sets?
4. How would the result change if we modified the number of people who like all three beverages?
5. How does this approach apply to real-world survey analysis?

**Tip:** When solving problems with overlapping groups, visual tools like Venn diagrams can be very helpful to organize and verify data.

ある酒造会社が、日本酒、ビール、ウィスキーのうち少なくとも一種類は好むという100人を対象にアンケートを取った資料として、次のデータを公表した：日本酒が好きな人は45人、ビールが好きな人は85人、ウィスキーが好きな人は60人、日本酒とビールだけが好きな人は30人、日本酒とウィスキーだけが好きな人は25人、ビールとウィスキーだけが好きな人は55人、3つとも好きな人は12人。この資料は信頼できるかどうか考えよ。

Analyze a beverage preference survey using set theory and the inclusion-exclusion principle. This problem requires understanding of overlapping sets and their intersections. Suitable for students in Grades 10-12.

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