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  2. www.cuemath.com › algebra › equivalence-relationsEquivalence Relation - Definition, Proof, Properties, Examples

    An equivalence relation is a binary relation defined on a set X such that the relations are reflexive, symmetric and transitive. If any of the three conditions (reflexive, symmetric and transitive) does not hold, the relation cannot be an equivalence relation.

  3. math.libretexts.org › Bookshelves › Mathematical7.2: Equivalence Relations - Mathematics LibreTexts

    Apr 17, 2022 · Definition: equivalence relation. Let A be a nonempty set. A relation ∼ on the set A is an equivalence relation provided that ∼ is reflexive, symmetric, and transitive. For a, b ∈ A, if ∼ is an equivalence relation on A and a ∼ b, we say that a is equivalent to b.

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  5. math.libretexts.org › Bookshelves › Combinatorics_and7.3: Equivalence Relations - Mathematics LibreTexts

    A relation on a set A is an equivalence relation if it is reflexive, symmetric, and transitive. We often use the tilde notation a∼b to denote an equivalence relation.

  6. math.libretexts.org › Bookshelves › Mathematical7.3: Equivalence Classes - Mathematics LibreTexts

    Apr 17, 2022 · An equivalence relation on a set is a relation with a certain combination of properties (reflexive, symmetric, and transitive) that allow us to sort the elements of the set into certain classes.

  7. www.whitman.edu › mathematics › higher_math_online5.1 Equivalence Relations - Whitman College

    Example 5.1.4 Let A be the set of all vectors in R2. If a, b ∈ A , define a ∼ b to mean that a and b have the same length; ∼ is an equivalence relation. . If ∼ is an equivalence relation defined on the set A and a ∈ A, let [a] = {x ∈ A: a ∼ x}, called the equivalence class corresponding to a.

  8. web.math.ucsb.edu › ~padraic › mathcamp_2014Lecture 3: Equivalence Relations - web.math.ucsb.edu

    Today's concepts are the ideas of sets and equivalence relations: 1 Sets. set, for the purposes of this lecture, is just some collection of objects1. We usually denote a set by listing its elements in between a pair of curly braces fg.

  9. personal.math.ubc.ca › ~lior › teachingEQUIVALENCE RELATIONS (NOTES FOR STUDENTS)

    Examples of this notation include: Equality:x = y;x 6= y Order: x < y (but we usually write y. x rather than x 6< y). Divisibility: ajb, a - b. 1.2.2. Formalization. We can encode relations using set theory. For this write X. X for Cartesian product, that is the set of pairs f(x;y) j x;y 2 Xg.

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