1. **Problem Statement:** Given a universal set $U$ with $n(U) = 10$ and a subset $A = \{2, 4, 6\}$, find the number of elements in the complement of $A$, denoted $n(A')$. 2. **Formula and Explanation:** The complement of a set $A$ in a universal set $U$ contains all elements in $U$ that are not in $A$. The formula to find the number of elements in the complement is: $$n(A') = n(U) - n(A)$$ where $n(U)$ is the number of elements in the universal set and $n(A)$ is the number of elements in set $A$. 3. **Calculate $n(A)$:** The set $A = \{2, 4, 6\}$ has 3 elements, so: $$n(A) = 3$$ 4. **Calculate $n(A')$:** Using the formula: $$n(A') = n(U) - n(A) = 10 - 3 = 7$$ 5. **Interpretation:** The complement of $A$ contains 7 elements, which are all elements in $U$ except 2, 4, and 6. **Final answer:** $n(A') = 7$ which corresponds to option c.