1. **State the problem:** Given the universal set $U = \{7, 8, 9, 10, 11, 12, 13\}$ and subset $A = \{7, 10, 12, 13\}$, find the complement of $A$, denoted $A'$. 2. **Recall the definition:** The complement $A'$ consists of all elements in $U$ that are not in $A$. Mathematically, $$A' = U \setminus A = \{x \in U : x \notin A\}$$ 3. **Find elements in $U$ not in $A$:** - $7$ is in $A$, exclude it. - $8$ is not in $A$, include it. - $9$ is not in $A$, include it. - $10$ is in $A$, exclude it. - $11$ is not in $A$, include it. - $12$ is in $A$, exclude it. - $13$ is in $A$, exclude it. 4. **Write the complement set:** $$A' = \{8, 9, 11\}$$ 5. **Interpretation:** The complement is not empty, so option A is correct with $A' = \{8, 9, 11\}$. Option B is incorrect because $A'$ is not the empty set.