1. The problem is to find the union of three sets: $A$, $B$, and $C$, specifically $(A \cup B) \cup C$. 2. The union of two sets $X$ and $Y$, denoted $X \cup Y$, is the set containing all elements that are in $X$, or in $Y$, or in both. 3. First, find $A \cup B$: $$A = \{4, 5, 6, 7, 8, 9\}$$ $$B = \{2, 4, 6, 8, 10, 12\}$$ Combine all unique elements: $$A \cup B = \{2, 4, 5, 6, 7, 8, 9, 10, 12\}$$ 4. Next, find $(A \cup B) \cup C$: $$C = \{1, 3, 5, 7, 9, 11, 13, 15\}$$ Combine all unique elements from $A \cup B$ and $C$: $$ (A \cup B) \cup C = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15\}$$ 5. This is the final union set containing all elements from $A$, $B$, and $C$ without duplicates. Answer: $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15\}$