Sets

Operations on Sets


  • Union of sets: A ∪ B = {x ∈ A or x ∈ B}
  • Intersection of sets: A ∩ B = {x ∈ A and x ∈ B}
  • Difference of sets: A – B = {x ∈ A and x ∉ B}
  • Symmetric difference: A Δ B = (A – B) ∪ (B – A) [or] (A ∪ B) – (A ∩ B)
  • Disjoint sets: A ∩ B = φ.
  • A – B ⊆ A and B – A ⊆ B.

View the Topic in this video From 38:06 To 48:48

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1. (i). Idempotent Law

         a) A ∪ A = A

         b) A ∩ A = A

(ii). Identity Law

     a) A ∪ φ = A

     b) A ∩ U = A

(iii). Commutative Law

     a) A ∪ B = B ∪ A

     b) A ∩ B = B ∩ A

(iv). Associative Law

     a) (A ∪ B) ∪ C = A ∪ (B ∪ C)

     b) A ∩ (B ∩ C) = (A ∩ B) ∩ C

(v). Distributive Law

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

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

2. a) A − (B ∩ C) = (A − B ) ∪ (A − C)

    b) A − (B ∪ C) = (A − B) ∩ (A − C)

3. a) (A − B) ∪ (B − A) = (A ∪ B) − (A ∩ B)

    b) A ∩ (B − C) = (A ∩ B) − (A ∩ C)

    c) A ∩ (B Δ C) = (A ∩ B) Δ (A ∩ C)

    d) (A ∩ B) ∪ (A − B) = A

    e) A ∪ (B − A) = (A ∪ B)