1. The problem asks for the number of elements in the union of two sets $S$ and $T$. 2. Given sets: $$S = \{a, b, c, d\}$$ $$T = \{c, d, e, f\}$$ 3. The union of two sets $S \cup T$ contains all elements that are in $S$, or in $T$, or in both. 4. To find $n(S \cup T)$, use the formula: $$n(S \cup T) = n(S) + n(T) - n(S \cap T)$$ 5. Calculate each term: - $n(S) = 4$ (elements: a, b, c, d) - $n(T) = 4$ (elements: c, d, e, f) - $S \cap T = \{c, d\}$ so $n(S \cap T) = 2$ 6. Substitute values: $$n(S \cup T) = 4 + 4 - 2$$ 7. Simplify: $$n(S \cup T) = \cancel{4} + \cancel{4} - 2 = 6$$ 8. Therefore, the number of elements in the union is 6. **Final answer:** C) 6