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De Morgan’s Law are based on complement of sets

  1. (A ∪ B)´ = A′ ∩ B′
  2. (A ∩ B)′ = A′ ∪ B′


Let us prove the law by Venn Diagrams

Let's take two sets A and B like

2 sets to prove demorgans law.jpg

Proving (A ∪ B)´ = A′ ∩ B′

De Morgans Law - Proving union of complement is equal to intersection of complements.jpg

Proving (A ∩ B)′= A′ ∪ B′

De Morgans Law - Proving intersection of complement is equal to union of complements.jpg

  1. Chapter 1 Class 11 Sets
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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.