Given A = {4, 5, 6}, B = {3, 4, 6, 7}, and C = {2, 3, 6}, verify the distributive
law of union over intersection and intersection over union. Also, verify by means of Venn
diagrams, with different orders of successive shading.draw simple and different venn diagrams for both

The distributive laws have been verified as follows:

1. **Union over intersection:**  
   \[
   A \cup (B \cap C) = (A \cup B) \cap (A \cup C)
   \]
   This holds true, as both sides are equal.

2. **Intersection over union:**  
   \[
   A \cap (B \cup C) = (A \cap B) \cup (A \cap C)
   \]
   This is also verified to be true.

The Venn diagrams shown visually represent these distributive laws. The first set of diagrams illustrates the union over intersection, and the second set shows the intersection over union, each confirming the equality.

Would you like further details on these operations, or do you have any questions?

Here are some related questions for further practice:
1. Can you verify the commutative property for these sets?
2. What is the result of \( A \cap (B \cap C) \)?
3. How would these laws behave for an empty set?
4. Can you prove the distributive law using set-builder notation?
5. What are the De Morgan’s laws for these sets?

**Tip:** Venn diagrams are a powerful tool for visualizing relationships between sets, helping to confirm algebraic set identities.

Given A = {4, 5, 6}, B = {3, 4, 6, 7}, and C = {2, 3, 6}, verify the distributive law of union over intersection and intersection over union. Also, verify by means of Venn diagrams, with different orders of successive shading. Draw simple and different Venn diagrams for both.

Explore how to verify the distributive law of union over intersection and intersection over union using the sets A = {4, 5, 6}, B = {3, 4, 6, 7}, and C = {2, 3, 6}. This guide includes key set theory concepts, step-by-step solutions, and visual verification through Venn diagrams. Suitable for high school students in Grades 9-12.

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