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To solve \( (A \cap B) \cup C \) using the given sets, let's follow these steps:

### Given sets:
- \( A = \{4, 5, 6, 7, 8, 9\} \)
- \( B = \{1, 3, 5, 7, 9, 11, 13, 15\} \)
- \( C = \{2, 5, 6, 9, 10, 12\} \)

### Step 1: Find \( A \cap B \) (Intersection of A and B)
The intersection of two sets is the set of elements common to both.

- Common elements between \( A \) and \( B \) are: \( \{5, 7, 9\} \)

Thus, \( A \cap B = \{5, 7, 9\} \).

### Step 2: Find \( (A \cap B) \cup C \) (Union of \( A \cap B \) and \( C \))
The union of two sets is the set of all distinct elements that are in either of the sets.

- Elements of \( (A \cap B) = \{5, 7, 9\} \)
- Elements of \( C = \{2, 5, 6, 9, 10, 12\} \)

The union of \( \{5, 7, 9\} \) and \( \{2, 5, 6, 9, 10, 12\} \) is:
- \( \{2, 5, 6, 7, 9, 10, 12\} \)

### Final Answer:
\( (A \cap B) \cup C = \{2, 5, 6, 7, 9, 10, 12\} \)

Let me know if you would like further details or have any questions!

### Follow-up Questions:
1. How do you find the difference between two sets, such as \( A - B \)?
2. What is the symmetric difference of sets, and how does it differ from the union?
3. How can you represent \( A \cap B \) using a Venn diagram?
4. What are the properties of set operations like commutativity or associativity in intersections and unions?
5. Can you find \( (A \cup B) \cap C \) and how does it differ from \( (A \cap B) \cup C \)?

### Tip:
When solving problems with sets, visualizing the sets using Venn diagrams can help make intersections and unions clearer!

Use the given sets to find (A ∩ B) ∪ C where A = {4, 5, 6, 7, 8, 9}, B = {1, 3, 5, 7, 9, 11, 13, 15}, and C = {2, 5, 6, 9, 10, 12}.

Find the union and intersection of sets A, B, and C using set theory. Given A = {4, 5, 6, 7, 8, 9}, B = {1, 3, 5, 7, 9, 11, 13, 15}, and C = {2, 5, 6, 9, 10, 12}, learn how to compute (A ∩ B) ∪ C with a detailed explanation.

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