Class 11 : Sets : Formulas

 

Laws of Algebra of Sets

Idempotent Laws: For any set A, we have

• A ∪ A = A
• A ∩ A = A

Identity Laws: For any set A, we have

• A ∪ Φ = A
• A ∩ U = A

Commutative Laws: For any two sets A and B, we have

• A ∪ B = B ∪ A
• A ∩ B = B ∩ A

Associative Laws: For any three sets A, B and C, we have

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

Distributive Laws: If A, B and Care three sets, then

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

De-Morgan’s Laws: If A and B are two sets, then

• (A ∪ B)’ = A’ ∩ B’
• (A ∩ B)’ = A’ ∪ B’

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Formulae to Solve Practical Problems on Union and Intersection Sets

Let A, B and C be any three finite sets, then

• n(A ∪ B) = n(A) + n (B) – n(A ∩ B)
• If (A ∩ B) = Φ, then n (A ∪ B) = n(A) + n(B)
• n(A – B) = n(A) – n(A ∩ B)
• n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)

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