Complement of a Set in Set Theory
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Questions and Answers

¿Cuál es el complemento del conjunto universal U?

  • Un conjunto vacío que no contiene elementos de U
  • El conjunto vacío ∅ (correct)
  • El conjunto U mismo
  • Un conjunto que contiene todos los elementos de U

    • ¿Cuál es la propiedad del complemento de un conjunto A?

  • (A')' = A (correct)
  • A' ∪ A = ∅
  • A' ∩ A = U
  • A' = A

    • ¿Cuál es la relación entre el complemento de la unión de dos conjuntos y el complemento de la intersección de los mismos conjuntos?

  • (A ∪ B)' = A' ∩ B' (correct)
  • (A ∩ B)' = A' ∩ B'
  • (A ∩ B)' = A' ∪ B'
  • (A ∪ B)' = A' ∪ B'

    • ¿Cuál es el resultado de encontrar el complemento del conjunto A = {1, 2, 3} en el conjunto universal U = {1, 2, 3, 4, 5, 6}?

    <p>{4, 5, 6}</p> Signup and view all the answers

    ¿Cuál es la relación entre el complemento de la intersección de dos conjuntos y el complemento de la unión de los mismos conjuntos?

    <p>(A ∩ B)' = A' ∪ B'</p> Signup and view all the answers

    Study Notes

    Complement of a Set

    Definition

    The complement of a set A, denoted as A' or Ac, is the set of all elements in the universal set U that are not in A.

    Properties

    • The complement of the universal set U is the empty set ∅.
    • The complement of the empty set ∅ is the universal set U.
    • For any set A, (A')' = A (double complement law).
    • For any sets A and B, (A ∪ B)' = A' ∩ B'.

    Operations

    • De Morgan's laws:
      • (A ∪ B)' = A' ∩ B'
      • (A ∩ B)' = A' ∪ B'
    • The complement of the union of two sets is the intersection of their complements.
    • The complement of the intersection of two sets is the union of their complements.

    Examples

    • If the universal set U = {1, 2, 3, 4, 5, 6} and A = {1, 2, 3}, then A' = {4, 5, 6}.
    • If the universal set U = {a, b, c, d, e} and B = {a, c, e}, then B' = {b, d}.

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    Description

    Learn about the definition, properties, and operations of the complement of a set in set theory, including De Morgan's laws and examples.

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