Proving Distributive law of sets by Venn Diagram

Last updated at April 16, 2024 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo