Sets

Complement of a Set


  • Complement of a set: A' = {x ∈ U and x ∉ B}
  • A ∪ A' = U and A ∩ A' = φ.
  • (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'

View the Topic in this video From 49:30 To 52:02

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1. De-Morgan's Law

    a) (A ∪ B)' = A' ∩ B'

    b) (A ∩ B)' = A' ∪ B'

2. a) A − B = A' ∩ B'

    b) B − A = B ∩ A'

3. a) U' = φ

    b) φ' = U

    c) (A')' = A

    d) A ∩ A' = φ

    e) A U A' = U

    f) A ⊆ B ⇔ B' ⊆ A'