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CBSE Class 11 Maths Notes: Sets – Algebra of Sets and Power Set

by Anand Meena
April 22, 2019
in 11th Class, Class Notes
Reading Time: 2min read
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Algebra of Sets:

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Idempotent Law: For any set A,

  • A ∪ A = A
  • A ∩ A = A

Identity Law: For any set A,

  • A ∪ ϕ = A
  • A ∩ U = A

Commutative Law: For any two sets A and B

  • A ∪ B = B ∪ A
  • A ∩ B = B ∩ A

Associative Law: For any three sets A, B and C

  • ≤ A ∪ B) ∪ C = A ∪ ≤ B ∪ C)
  • A ∩ ≤ B ∩ C) = ≤ A ∩ B) ∩ C

Distributive Law: For any three sets A, B and C

  • A ∪ ≤ B ∩ C) = ≤ A ∪ B) ∩ ≤ A ∪ C)
  • A ∩ ≤ B ∪ C) = ≤ A ∩ B) ∪ ≤ A ∩ C)

De Morgan’s Law: For any two sets A and B

  • ≤ A ∪ B)¢ = A¢ ∩ B¢
  • ≤ A ∩ B)¢ = A¢ ∪ B¢

POWER SET

The set of all subsets of a given set A is called the power set A and is denoted by P ≤ A). P ≤ A) = {S: S ⊆ A}

For example, if A = {1, 2, 3}, then

P≤ A) = { ϕ,{1},{2},{3},{1},{1,2},{1,3},{2.3},{1,2,3}}

Clearly, if A has n elements, then its power set P≤ A) contains exactly 2n elements.

Some More Results:

  • n ≤ set of elements neither in A nor in B) = n ≤ A¢ ∩ B¢) = n≤ A ∪ B)¢ = n ≤ U) – n ≤ A ∪ B)
  • n ≤ A¢ ∪ B¢) = n≤ A ∩ B)¢ = n ≤ U) – n ≤ A ∩ B)
  • n ≤ A Δ B) = n [≤ A – B) ∪ ≤ B – A)] = n [≤ A ∩ B¢) ∪ ≤ A¢ ∩ B)] = n ≤ A)         + n ≤ B)         – 2n≤ A ∩ B).
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CBSE Class 11 Maths Sets Relations and Functions All Topic Notes CBSE Class 11 Maths All Chapters Notes

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Tags: CBSE 11 NotesCBSE NotesClass 11 NotesClass 11thClass 11th NotesFree Notes

Anand Meena

Full time entrepreneur, likes to indulge in writing reviews about the latest technologies apart from helping students in career and exam related topics.

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