1. **Problem Statement:** Identify which set operation corresponds to the shaded region in the given Venn diagram involving sets $A$, $B$, and universal set $U$. 2. **Recall Set Operations:** - $A \cup B$ is the union of $A$ and $B$ (all elements in $A$ or $B$). - $A \cap B$ is the intersection of $A$ and $B$ (elements in both $A$ and $B$). - $\overline{B}$ is the complement of $B$ (elements not in $B$). 3. **Analyze Options:** - Option 1: $A \cup \overline{B}$ means all elements in $A$ or not in $B$. - Option 2: $A \cap \overline{B}$ means elements in $A$ but not in $B$. - Option 3: $\overline{A} \cup B$ means elements not in $A$ or in $B$. - Option 4: $\overline{A} \cap B$ means elements not in $A$ but in $B$. - Options 5 and 6 are complements of options 1 and 2 respectively. - Option 7: $(A \cap \overline{B}) \cup (A \cap B) = A$ (since union of parts of $A$). - Option 8: $(A \cap \overline{B}) \cup (A \cup B) = A \cup B$ (since $A \cup B$ includes all). - Options 9 and 10 are intersections involving $(A \cap \overline{B})$ and other sets. 4. **Interpretation:** - The shaded region corresponds to elements in $A$ but not in $B$. - This matches $A \cap \overline{B}$. 5. **Final Answer:** Option 2. $$\boxed{2}$$