We are given the total number of elements in the universal set $n(S) = 40$, as well as the number of elements in sets $A$, $B$, and $C$ with:

• $n(A) = 16$
• $n(B) = 11$
• $n(C) = 32$

Let's define the variables:

• $x$: Represents the number of elements that are in all three sets $A \cap B \cap C$.
• $y$: Represents the number of elements in $A \cap B$ but not in $C$.
• $z$: Represents the number of elements in $B \cap C$ but not in $A$.
• $w$: Represents the number of elements in $A \cap C$ but not in $B$.

To solve this problem, we need more details on the relationships between the sets. The hint indicates an example (likely a solved Venn diagram) is provided, but without specific overlap information, we can't solve for $x$, $y$, $z$, and $w$ directly. These variables typically represent intersections between sets, but we would need the number of elements in the pairwise or three-way intersections to continue.

If additional intersection data or relationships are available, I can continue solving it step-by-step.

Would you like me to explain this further or provide clarification on any part of the Venn diagram setup?

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Here are five questions you can explore next:

1. How are the elements distributed between two sets, $A$ and $B$, in a Venn diagram?
2. What is the significance of the intersection $A \cap B \cap C$ in a Venn diagram?
3. How do the union and intersection operations affect the total number of elements in the sets?
4. How would adding a fourth set $D$ change the structure of a Venn diagram?
5. What strategies can help when solving more complex Venn diagram problems?

Tip: In Venn diagrams, always try to find the intersections first, as they help break down the problem into smaller parts.