Set Theory: Intersection of Sets
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Questions and Answers

What is the intersection of two sets A and B denoted by?

  • A ∩ B (correct)
  • B - A
  • A ∪ B
  • A - B
  • Which property states that A ∩ B = B ∩ A?

  • Distributive Property
  • Commutative Property (correct)
  • Union Property
  • Associative Property
  • If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

  • {1, 2, 3, 4}
  • {1, 4}
  • {2, 3} (correct)
  • What is the intersection of a set with itself?

    <p>The set itself</p> Signup and view all the answers

    What is represented by the region common to both circles in a Venn diagram?

    <p>The intersection of two sets</p> Signup and view all the answers

    Study Notes

    Intersection of Sets

    Definition

    • The intersection of two or more sets is a set containing all elements that are common to all the sets.

    Notation

    • The intersection of sets A and B is denoted by A ∩ B.

    Properties

    • Commutative Property: A ∩ B = B ∩ A
    • Associative Property: (A ∩ B) ∩ C = A ∩ (B ∩ C)
    • Distributive Property: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

    Examples

    • If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}
    • If A = {a, b, c} and B = {b, c, d}, then A ∩ B = {b, c}

    Important Points

    • The intersection of two sets can be empty if they do not have any common elements.
    • The intersection of a set with itself is the set itself, i.e., A ∩ A = A.
    • The intersection of a set with the universal set is the set itself, i.e., A ∩ U = A.

    Venn Diagram Representation

    • The intersection of two sets is represented by the region common to both circles in a Venn diagram.

    Definition

    • Intersection of sets consists of elements common to all sets involved.

    Notation

    • Denoted by A ∩ B for the intersection of sets A and B.

    Properties

    • Commutative Property: Order does not matter, A ∩ B = B ∩ A.
    • Associative Property: Grouping does not affect the result, (A ∩ B) ∩ C = A ∩ (B ∩ C).
    • Distributive Property: Combines intersection and union, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

    Examples

    • For sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection A ∩ B yields {2, 3}.
    • For A = {a, b, c} and B = {b, c, d}, the intersection results in {b, c}.

    Important Points

    • The intersection can be empty if there are no common elements.
    • Intersection of a set with itself is the set: A ∩ A = A.
    • Intersection with the universal set provides the original set: A ∩ U = A.

    Venn Diagram Representation

    • In Venn diagrams, the intersection is visually represented by the overlapping region of the circles corresponding to the sets involved.

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    Description

    Understand the definition, notation, properties, and examples of the intersection of two or more sets in set theory. Learn about the commutative, associative, and distributive properties.

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