1. The problem is to understand and represent the set expression $A \cap (B \cap C^\prime)^\prime$ on a Venn diagram. 2. Let's break down the expression step-by-step: - $C^\prime$ means the complement of set $C$, i.e., all elements not in $C$. - $B \cap C^\prime$ means elements that are in $B$ but not in $C$. - $(B \cap C^\prime)^\prime$ means the complement of the set $B \cap C^\prime$, i.e., all elements not in $B$ or in $C$. - Finally, $A \cap (B \cap C^\prime)^\prime$ means elements that are in $A$ and also in the complement of $B \cap C^\prime$. 3. To visualize this on a Venn diagram with three sets $A$, $B$, and $C$: - Shade the region representing $B \cap C^\prime$ (inside $B$ but outside $C$). - Then shade the complement of this region (everything outside $B \cap C^\prime$). - Finally, find the intersection of this complement with $A$ (the part of $A$ that is not in $B \cap C^\prime$). 4. This results in the part of $A$ excluding the portion that lies in $B$ but outside $C$. 5. The final answer is the set $A$ excluding the elements that are in $B$ but not in $C$. This is the interpretation and representation of $A \cap (B \cap C^\prime)^\prime$ on a Venn diagram.