1. **Problem:** Find $B \cup C$ where $B = \{1,3,5,7\}$ and $C = \{3,4,5\}$. 2. **Formula and rules:** The union of two sets $B$ and $C$, denoted $B \cup C$, is the set of all elements that are in $B$, or in $C$, or in both. 3. **Work:** List all unique elements from both sets: $$B \cup C = \{1,3,5,7\} \cup \{3,4,5\} = \{1,3,4,5,7\}$$ 4. **Explanation:** We combine all elements from both sets without repeating any element. The elements 3 and 5 appear in both sets but are listed only once in the union. **Final answer:** $$B \cup C = \{1,3,4,5,7\}$$