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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)

Distributive law proof by venn diagram.jpg



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


  1. Chapter 1 Class 11 Sets
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.