https://file.aiquickdraw.com/mathbot/file/1725503777866ruyjf9x4.jpg

We are given three sets:  
- \( P = \{1, 3, 5, 7\} \)  
- \( Q = \{3, 5\} \)  
- \( R = \{5, 7, 9\} \)

The question asks for the union of \( P \cup Q \cup R \). To solve this, we need to combine all the unique elements from these three sets.

### Step-by-Step Solution:
- Elements of \( P \): \( 1, 3, 5, 7 \)
- Elements of \( Q \): \( 3, 5 \)  
- Elements of \( R \): \( 5, 7, 9 \)

Now, combining the elements of \( P \cup Q \cup R \), we list all distinct elements:
\[ P \cup Q \cup R = \{1, 3, 5, 7, 9\} \]

Therefore, the correct answer is \( \{1, 3, 5, 7, 9\} \), which matches **Option 4**.

### Do you need any further details or have questions on this?

Here are 5 related questions to expand on this topic:
1. What is the intersection of \( P \cap Q \)?
2. How do you compute the difference between two sets, for example, \( P - R \)?
3. What is the complement of a set in set theory?
4. How does the union operation differ from the intersection operation?
5. What happens when the union involves an empty set?

**Tip:** When calculating unions, remember that duplicates are not included; only unique elements matter!

If P = {1, 3, 5, 7}, Q = {3, 5} and R = {5, 7, 9}, then P ∪ Q ∪ R = ?

This problem involves finding the union of three sets P, Q, and R. Learn how to combine all distinct elements from sets {1, 3, 5, 7}, {3, 5}, and {5, 7, 9} to get the correct result. Suitable for students in Grades 7-10.

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