Equivalence Relations Quiz
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Questions and Answers

Which of the following best describes an equivalence relation in mathematics?

  • A relation that is only transitive
  • A relation that is reflexive, symmetric, and transitive (correct)
  • A relation that is only symmetric
  • A relation that is only reflexive

    • What is an example of an equivalence relation in geometry?

  • The equipollence relation between line segments (correct)
  • The relation between a line segment and an angle
  • The relation between a point and a line
  • The relation between two different line segments

    • Which of the following is NOT a property of an equivalence relation?

  • Symmetry
  • Transitivity
  • Antisymmetry (correct)
  • Reflexivity

    • What does an equivalence relation provide for a set?

    <p>A partition into disjoint equivalence classes</p> Signup and view all the answers

    Which notation is commonly used to denote that two elements are equivalent with respect to an equivalence relation?

    <p>a ∼ b</p> Signup and view all the answers

    Which of the following best describes an equivalence relation?

    <p>A relation that is reflexive, symmetric, and transitive</p> Signup and view all the answers

    What is an example of an equivalence relation in geometry?

    <p>The equipollence relation between line segments</p> Signup and view all the answers

    What does an equivalence relation provide for a set?

    <p>A partition of the set into disjoint equivalence classes</p> Signup and view all the answers

    Which notation is commonly used to denote that two elements are equivalent with respect to an equivalence relation?

    <p>a ∼ b</p> Signup and view all the answers

    What is the reflexive property of an equivalence relation?

    <p>Any element is equivalent to itself</p> Signup and view all the answers

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