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In the image, the question seems to involve set theory. Here's the question, extracted for clarity:

- Let the Universal Set \( S \) have 87 elements.
- Set \( A \) and \( B \) are subsets of \( S \).
- Set \( A \) contains 43 elements, and Set \( B \) contains 35 elements.
- If Sets \( A \) and \( B \) have 26 elements in common, how many elements are in \( A \) but not in \( B \)?

### Solution Approach:

The number of elements in \( A \) but not in \( B \) is represented by \( |A \setminus B| \), which is the difference between the number of elements in \( A \) and the number of elements that \( A \) shares with \( B \) (i.e., the intersection of \( A \) and \( B \)).

Given:
- \( |A| = 43 \) (the number of elements in set \( A \)),
- \( |B| = 35 \) (the number of elements in set \( B \)),
- \( |A \cap B| = 26 \) (the number of elements common to both \( A \) and \( B \)).

To find \( |A \setminus B| \) (the elements in \( A \) but not in \( B \)):
\[
|A \setminus B| = |A| - |A \cap B|
\]
Substitute the known values:
\[
|A \setminus B| = 43 - 26 = 17
\]

Thus, there are **17 elements** in set \( A \) but not in set \( B \).

Would you like more details or further clarification on any step?

### Follow-up Questions:
1. How would you calculate the number of elements in \( B \setminus A \)?
2. Can you find how many elements are in \( A \cup B \) (the union of sets \( A \) and \( B \))?
3. What would be the result if \( A \) and \( B \) had no elements in common?
4. How can we express \( |A \cup B| \) using the inclusion-exclusion principle?
5. How does the universal set \( S \) influence this problem, if at all?

### Tip:
When dealing with set theory, the inclusion-exclusion principle is very useful for handling problems involving unions and intersections of sets.

Let the Universal Set S have 87 elements. A and B are subsets of S. Set A contains 43 elements, and Set B contains 35 elements. If A and B have 26 elements in common, how many elements are in A but not in B?

Learn how to solve a set theory problem involving the number of elements in set A but not in set B. This example covers set subtraction, the inclusion-exclusion principle, and intersection of sets. Suitable for high school students in Grades 9-12.

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