The First Distributive Law
Explore the first distributive law in set theory, which explains how the union operation distributes over intersection. Learn to prove this law using set membership, visualize it with Venn diagrams, and apply it to examples. Verify the law with practical Python programming exercises to deepen your understanding of fundamental set operations.
There are two distributive laws of sets. The first law shows how the union operation distributes over the intersection operation. The second law shows us how the intersection operation distributes over the union operation. For the arbitrary sets
Let’s analyze the first distributive law and see the reason why it holds.
Distribution of the union over an intersection
We can take an arbitrary element belonging to the set on the left-hand side and show its membership in the set on the right-hand side and vice versa. First, we show that