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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′= ∅

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.