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The problem you've shared involves set theory and can be solved using the principle of inclusion and exclusion. Let's break it down:

### Information provided:
- \( |S| = 93 \) (The universal set has 93 elements)
- \( |A| = 26 \) (Set \( A \) contains 26 elements)
- \( |B| = 19 \) (Set \( B \) contains 19 elements)
- \( |A \cup B| = 44 \) (The number of elements in \( A \) or \( B \) is 44)
  
The goal is to find how many elements are in \( B \) but not in \( A \), which is represented by \( |B \setminus A| \).

### Step-by-step solution:

1. The total number of elements in either \( A \) or \( B \) is given by the union formula:
   \[
   |A \cup B| = |A| + |B| - |A \cap B|
   \]
   Plugging in the known values:
   \[
   44 = 26 + 19 - |A \cap B|
   \]
   Simplifying:
   \[
   44 = 45 - |A \cap B|
   \]
   Therefore, the number of elements common to both \( A \) and \( B \) (i.e., \( |A \cap B| \)) is:
   \[
   |A \cap B| = 45 - 44 = 1
   \]

2. Now, to find how many elements are in \( B \) but not in \( A \) (i.e., \( |B \setminus A| \)), we subtract the number of elements in \( A \cap B \) from the total number of elements in \( B \):
   \[
   |B \setminus A| = |B| - |A \cap B| = 19 - 1 = 18
   \]

### Final Answer:
There are **18 elements** in \( B \) but not in \( A \).

Would you like further clarification or details on this? 

Here are five related questions to explore:
1. How many elements are in \( A \cap B \)?
2. What is the number of elements in \( A \setminus B \)?
3. How many elements are in \( S \setminus (A \cup B) \)?
4. What would happen if \( |A \cup B| \) was different?
5. How do we compute \( |A \cup B| \) for more than two sets?

**Tip**: The principle of inclusion and exclusion is powerful for solving problems involving multiple sets. It allows us to account for overlaps and avoid overcounting.

Let the Universal Set, S, have 93 elements. A and B are subsets of S. Set A contains 26 elements and Set B contains 19 elements. If the total number of elements in either A or B is 44, how many elements are in B but not in A?

Learn how to solve a set theory problem involving the universal set S, subsets A and B, and using the principle of inclusion-exclusion. The problem is suitable for students in Grades 9-12.

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