Tag: commutative

  • Mastering Set Notations and DeMorgan’s Law: A Comprehensive Guide

    Mastering Set Notations and DeMorgan’s Law: A Comprehensive Guide

    The commutative laws

    A ∪ B = B ∪ A

    A ∩ B = B ∩ A

    Associative laws

    (A ∪ B) ∪ C = A ∪ (B ∪ C)

    (A ∩ B) ∩ C = A ∩ (B ∩ C)

    Distributive laws

    A ∩ (B ∪ C) = (A ∩ B)U (A ∩ C)

    A U (B ∩ C ) = (A ∪ B) ∩ (A ∪ C)

    Idempotent laws

    A U A = A

    A ∩ A = A

    Identity laws

    A ∪ ∅ = A

    A ∩ U = A

    Universal Bound laws

    A ∪ U= U

    A ∪ ∅ = ∅

    DeMorgan’s law

    (A ∪ B)c = Ac ∩ Bc

    (A ∩ B)c = Ac ∪ Bc

    Complement laws

    A ∪ Ac = U

    (A ∩ A)c = ∅

    complement of U and ∅

    Uc = ∅

    c= ∪

    Double Complement law

    (Ac)c =A

    Set Difference law

    A – B = A ∩ Bc


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