There are 38
 students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to Spain or France but not Germany?

11
 members have visited Germany
18
 have been to Spain
18
 have visited France
7
 have been to Germany and France
8
 have only been to Spain
2
 have only been to Germany
5
 have been to only Spain and France
3
 have been to all three countries
Some of the members have not been to any of the three

We are tasked with determining how many students have been to Spain or France but not Germany. Here's how to break this down step by step, using the information provided.

### Step 1: Information Review
1. Total students: 38.
2. Germany: 11 students.
3. Spain: 18 students.
4. France: 18 students.
5. Germany and France: 7 students.
6. Only Spain: 8 students.
7. Only Germany: 2 students.
8. Only Spain and France: 5 students.
9. All three countries (Germany, France, and Spain): 3 students.
10. Some students haven't visited any of the three countries.

### Step 2: Analyze Sets
We want to find the number of students who visited **Spain or France but not Germany**.

#### Set Analysis:
- **Only Spain**: We are already given that 8 students have visited only Spain.
- **Only Spain and France**: 5 students have visited both Spain and France, but **not Germany**.
- **Only France**: To find how many visited **only France**, we use this logic:
  - France total = 18.
  - France and Germany = 7.
  - France, Spain, and Germany = 3 (already counted in Germany and France group).
  \[
  \text{Only France} = 18 - 7 - 3 = 8.
  \]

### Step 3: Total for Spain or France but not Germany
Now, we sum up all the students who have been to Spain or France but **not Germany**:
1. Only Spain: 8.
2. Only Spain and France: 5.
3. Only France: 8.

So, the total number of students who visited **Spain or France but not Germany** is:
\[
8 (\text{Only Spain}) + 5 (\text{Only Spain and France}) + 8 (\text{Only France}) = 21.
\]

### Final Answer:
**21 students** have been to Spain or France but not Germany.

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Do you want further details or have any questions?

Here are some related questions for further understanding:
1. How would the solution change if a fourth country was added to the analysis?
2. What if the number of students who visited only Spain doubled?
3. How many students visited only Germany or only Spain?
4. How would you calculate the total number of students who have not visited any of the countries?
5. What percentage of students visited both Spain and France but not Germany?

**Tip**: When dealing with Venn diagrams, it is helpful to break complex sets into smaller, easier-to-manage groups.

There are 38 students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to Spain or France but not Germany?

11 members have visited Germany
18 have been to Spain
18 have visited France
7 have been to Germany and France
8 have only been to Spain
2 have only been to Germany
5 have been to only Spain and France
3 have been to all three countries
Some of the members have not been to any of the three.

Find how many students from a travel club have been to Spain or France but not Germany. Explore this problem using set theory, Venn diagrams, and the principle of inclusion-exclusion. Suitable for Grades 9-11.

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