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The problem you're facing appears to involve a Venn diagram or a set theory problem based on students taking different classes. Let's break down the information given:

1. **Total number of students**: 38
2. **Students taking different subjects**:
   - 17 students are taking Math.
   - 21 students are taking English.
   - 15 students are taking History.
   - 9 students are taking both Math and English.
   - 7 students are taking both Math and History.
   - 8 students are taking both English and History.
   - 5 students are taking all three subjects: Math, English, and History.

### Objective:
You need to find out how many students are taking Math, but not English.

### Approach:

To solve this, we'll use the principle of inclusion-exclusion (PIE):

1. **Total students taking Math**:
   \[
   |M| = 17
   \]

2. **Students taking both Math and English**:
   \[
   |M \cap E| = 9
   \]

3. **Students taking both Math and History**:
   \[
   |M \cap H| = 7
   \]

4. **Students taking all three subjects (Math, English, and History)**:
   \[
   |M \cap E \cap H| = 5
   \]

We need to find the number of students taking Math but not English. We calculate this using:

\[
|M \setminus E| = |M| - |M \cap E| + |M \cap E \cap H|
\]

So,

\[
|M \setminus E| = 17 - 9 + 5 = 13
\]

Thus, **13 students are taking Math but not English**.

Would you like a detailed explanation of how we applied the principle of inclusion-exclusion or have any other questions?

### Related Questions:
1. How many students are taking English but not Math?
2. How many students are taking History but not Math or English?
3. How many students are taking at least one subject?
4. How many students are taking exactly two subjects?
5. How many students are not taking any of the three subjects?

### Tip:
For problems involving multiple sets and overlapping categories, always consider using a Venn diagram or the principle of inclusion-exclusion to simplify the problem-solving process.

A group of 38 students were surveyed about the courses they were taking in their college, resulting in the following results:
- 17 students were taking Math.
- 21 students were taking English.
- 15 students were taking History.
- 9 students said they were taking both Math and English.
- 7 students said they were taking both Math and History.
- 8 students said they were taking both English and History.
- 5 students said they were taking all three classes.
How many students took Math, but not English?

Solve a set theory problem involving students taking Math, English, and History. Apply the principle of inclusion-exclusion to determine how many students are taking Math but not English. Suitable for Grades 9-12.

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