Proving Distributive law of sets by Venn Diagram

Last updated at July 20, 2026 by

Distributive law of set is

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C )

 

Let us prove it by Venn diagram

 

Let’s take 3 sets – A, B, C

Proving Distributive law of sets by Venn Diagram - Intersection of Sets

We have to prove

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Proving Distributive law of sets by Venn Diagram - Part 2

 

 

Distributive law is also

 

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C )

this can also be proved in the same way.

Proof using examples is done here

 

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