https://file.aiquickdraw.com/mathbot/file/1728905834567vendil6h.jpg

It looks like you're working on a problem involving set operations, specifically unions, and using Venn diagrams to visualize relationships between the sets \(M\), \(N\), and \(K\).

The task seems to involve matching set equations with corresponding Venn diagrams. The equations in the image involve union operations (denoted by \(\cup\)) between different sets.

Here is an explanation of the general approach for matching the equations:

1. **\(M \cup N = N \cup M\)**: This is the **commutative property of union**, which means the order of sets in the union does not matter. Any diagram showing the union of \(M\) and \(N\) should match this equation.

2. **\(M \cup K = K \cup M\)**: Again, this uses the commutative property, but with sets \(M\) and \(K\). The diagram should display the union of \(M\) and \(K\), and the regions covered by both should be the same regardless of order.

3. **\(K \cup N = N \cup K\)**: Another commutative property, this time with sets \(K\) and \(N\). The Venn diagram that illustrates the union of \(K\) and \(N\) should be chosen.

4. **\((M \cup K) \cup N = M \cup (K \cup N)\)**: This is the **associative property** of union, where the grouping of sets does not affect the result. The Venn diagram should depict the union of all three sets \(M\), \(K\), and \(N\).

To match these correctly, examine the Venn diagrams to see which regions are shaded and check if the corresponding areas match the set operations in the equations.

Would you like me to further explain how to read these specific Venn diagrams, or help you solve this problem step by step?

Match the given set operations with their corresponding Venn diagrams, using the union operation.

Learn how to match set operations, involving the union of sets, with their corresponding Venn diagrams. This problem focuses on key set theory properties such as the commutative and associative laws of union, suitable for students in Grades 9-11.

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