1. **State the problem:** We are given universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ and subsets $A = \{1, 2, 3, 4, 5, 10\}$, $B = \{3, 4, 6, 8, 10\}$, and $C = \{4, 5, 6, 7, 9, 10\}$. We need to find the elements in $(A \cap B') \cap C$. 2. **Recall definitions:** - $B'$ is the complement of $B$ in $U$, i.e., elements in $U$ not in $B$. - $\cap$ denotes intersection, elements common to both sets. 3. **Find $B'$:** $$B' = U \setminus B = \{1, 2, 5, 7, 9, 11, 12\}$$ 4. **Find $A \cap B'$:** $$A \cap B' = \{1, 2, 3, 4, 5, 10\} \cap \{1, 2, 5, 7, 9, 11, 12\} = \{1, 2, 5\}$$ 5. **Find $(A \cap B') \cap C$:** $$\{1, 2, 5\} \cap \{4, 5, 6, 7, 9, 10\} = \{5\}$$ 6. **Final answer:** The elements in $(A \cap B') \cap C$ are $\boxed{5}$.