Let S be the universal set, where: S = /1, 2,3,.. 23,24, 25] Let sets A and B be subsets of S, where:
set A = /3, 4, 7, 9, 11, 14, 15, 17, 18,
Set B N f9, 12, 14, 18, 19, 20, 21, 23, 24, 25)
Find the number of elements in the set (A U B)

To find the number of elements in the set \( A \cup B \) (the union of sets \( A \) and \( B \)), we need to determine all unique elements in either set \( A \), set \( B \), or both.

### Given Sets:
- \( A = \{ 3, 4, 7, 9, 11, 14, 15, 17, 18 \} \)
- \( B = \{ 9, 12, 14, 18, 19, 20, 21, 23, 24, 25 \} \)

### Step-by-Step Process:

1. **List all elements in \( A \cup B \) (the union of \( A \) and \( B \))**:  
   The union operation combines all elements in both sets without duplicates:
   \[
   A \cup B = \{ 3, 4, 7, 9, 11, 12, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25 \}
   \]

2. **Count the unique elements**:  
   Now we count the number of unique elements in this union set:
   \[
   \text{Number of elements in } A \cup B = 16
   \]

### Final Answer:
The number of elements in \( A \cup B \) is **16**.

Would you like a detailed breakdown of how to find \( A \cap B \) (intersection) or any other aspects?

Here are some follow-up questions related to set theory:

1. What is the number of elements in the set \( A \cap B \) (intersection of sets \( A \) and \( B \))?
2. What is the number of elements in the set \( A \setminus B \) (elements in \( A \) but not in \( B \))?
3. How do we find the number of elements in the set \( S \setminus (A \cup B) \) (complement of the union)?
4. What is the difference between \( A \cup B \) and \( A \cap B \)?
5. How can we find the symmetric difference between sets \( A \) and \( B \)?

**Tip**: When dealing with unions and intersections, organizing elements carefully and removing duplicates will help avoid mistakes!

Let S be the universal set, where: S = [1, 2, 3, ..., 25]. Let sets A and B be subsets of S, where: set A = {3, 4, 7, 9, 11, 14, 15, 17, 18}, Set B = {9, 12, 14, 18, 19, 20, 21, 23, 24, 25}. Find the number of elements in the set (A ∪ B).

Explore the solution to finding the number of elements in the union of sets A and B, where A = {3, 4, 7, 9, 11, 14, 15, 17, 18} and B = {9, 12, 14, 18, 19, 20, 21, 23, 24, 25}. Learn the key concepts of set theory, including union and how to count unique elements. Suitable for students in Grades 6-8.

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