https://file.aiquickdraw.com/mathbot/file/1724403990834m4fdk2bo.jpg

To solve the problem shown in the image, I'll first transcribe and interpret the mathematical content.

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**Problem:**

Given the sets \( A = \{1, 2, 3\} \) and \( B = \{2, 3, 4\} \), identify the set that represents \( A \cup B \), which is the union of sets \( A \) and \( B \).

**Choices:**

A. \( \{1, 2\} \)  
B. \( \{2, 3\} \)  
C. \( \{1, 2, 3, 4\} \)  
D. \( \{1, 3\} \)

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### Solution:

The union of two sets \( A \) and \( B \) (denoted as \( A \cup B \)) is a set that contains all the elements from both sets \( A \) and \( B \), without repeating any element.

Given:
- \( A = \{1, 2, 3\} \)
- \( B = \{2, 3, 4\} \)

Now, let's find \( A \cup B \):

\[ A \cup B = \{1, 2, 3\} \cup \{2, 3, 4\} = \{1, 2, 3, 4\} \]

This is because:
- 1 is in \( A \)
- 2 is in both \( A \) and \( B \)
- 3 is in both \( A \) and \( B \)
- 4 is in \( B \)

Thus, the correct answer is:

**C. \( \{1, 2, 3, 4\} \)**

Would you like more details or have any further questions? 

Here are five related questions to expand on this topic:
1. What is the difference between the union and intersection of two sets?
2. How do you find the intersection of two sets \( A = \{1, 2, 3\} \) and \( B = \{2, 3, 4\} \)?
3. Can the union of two sets ever result in a set smaller than either of the original sets?
4. How does the concept of set union extend to more than two sets?
5. What is the difference between a union of sets and a Cartesian product of sets?

**Tip:** The union of two sets always contains all elements from both sets, with duplicates removed.

Explore the concept of set union with a detailed explanation and example. Learn how to find the union of sets A = {1, 2, 3} and B = {2, 3, 4}, and understand its relevance in mathematics. Suitable for students in Grades 7-9.

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