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!