Let's match the formulas with the corresponding Venn diagrams by analyzing both the set operations and the shaded areas.

Formula 1: $M \cup N = N \cup M$

• Explanation: This is the commutative property of the union. The union of $M$ and $N$ includes all elements that belong to either set.
• Matching Diagram: Look for a Venn diagram where both the regions of $M$ and $N$ are fully shaded. The position of the sets doesn't matter because of the commutative property.

Formula 2: $M \cup K = K \cup M$

• Explanation: Again, the commutative property, but this time between sets $M$ and $K$. The union should include all areas covered by either set $M$ or set $K$.
• Matching Diagram: Look for a Venn diagram where both the regions of $M$ and $K$ are fully shaded.

Formula 3: $K \cup N = N \cup K$

• Explanation: Another commutative property between $K$ and $N$. The union includes all elements that belong to either set $K$ or $N$.
• Matching Diagram: Look for a Venn diagram where the regions of $K$ and $N$ are fully shaded.

Formula 4: $(M \cup K) \cup N = M \cup (K \cup N)$

• Explanation: This is the associative property of union. The union of all three sets should be the same, no matter how you group them.
• Matching Diagram: The Venn diagram for this formula should show the union of all three sets $M$, $K$, and $N$, meaning the entire area covered by all three circles should be shaded.

Now, matching each formula with the diagrams:

1. $M \cup N = N \cup M$: This matches with the first diagram (top-right), where both $M$ and $N$ are shaded.
2. $M \cup K = K \cup M$: This corresponds to the second diagram (second row, right), where both $M$ and $K$ are shaded.
3. $K \cup N = N \cup K$: This matches the third diagram (third row, right), where $K$ and $N$ are shaded.
4. **((M \cup K) \cup N = M \cup (K