The Second Distributive Law
Explore the second distributive law in set theory which shows how intersection distributes over union. Understand its proof using subset relations and visualize it with Venn diagrams. Apply the law with practical examples and verify it programmatically using Python sets to solidify your grasp of fundamental set operations.
Let’s discuss the second distributive law and why it holds. It states that an intersection distributes over a union in the following manner:
The distribution of an intersection over a union
To see why the second distributive law holds, first, we must show that the set on the left-hand side is a subset of the set on the right-hand side:
Now, we show that the set on the right is a subset of the set on the left: