1. **State the problem:** Given the universal set $U = \{7, 8, 9, 10, 11, 12, 13\}$ and subset $A = \{9, 11, 12, 13\}$, find the complement of $A$, denoted $A'$. 2. **Recall the definition:** The complement of a set $A$ with respect to $U$ is the set of all elements in $U$ that are not in $A$. Mathematically, $$A' = \{x \in U : x \notin A\}$$ 3. **Identify elements not in $A$:** From $U$, remove all elements of $A$. Elements in $U$: 7, 8, 9, 10, 11, 12, 13 Elements in $A$: 9, 11, 12, 13 Elements not in $A$: 7, 8, 10 4. **Write the complement:** $$A' = \{7, 8, 10\}$$ 5. **Conclusion:** The complement $A'$ is the set $\{7, 8, 10\}$, which corresponds to choice A.