Complement of set A means

all elements of Universal set which are not in A

It is denoted by A’

 

Let A = {1, 2, 3, 4} , B = {3, 4, 5, 6}, C = {6, 7, 8}

and Universal set = U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A’ = U – A

A’ = { 1, 2, 3, 4 , 5, 6, 7, 8, 9, 10} – { 1, 2, 3, 4 }

A’ = {5, 6, 7, 8, 9, 10}

Complement of Set - Venn Diagram.jpg


Properties of Complement

  1. Complement laws:
    (i) A ∪ A′= U (ii) A ∩ A′= ∅
  2. De Morgan’s law :
    (i) (A ∪ B)´ = A′ ∩ B′ (ii) (A ∩ B)′= A′ ∪ B′
  3. Law of double complementation :
    (A′)′= A
  4. Laws of empty set and universal set
    ∅′ = U and U′= ∅
  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 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
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