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- An equivalence relation is a relation that is reflexive, symmetric, and transitive12. Examples of equivalence relations include12:
- The sign of ‘is equal to (=)’ on a set of numbers, characters, or symbols. For example, 1/3 = 3/9.
- For a given set of triangles, the relation of ‘is similar to (~)’ and ‘is congruent to (≅)’ shows equivalence.
- For a given set of integers, the relation of ‘congruence modulo n (≡)’ shows equivalence.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Equivalence relations can be explained in terms of the following examples:
- The sign of ‘is equal to (=)’ on a set of numbers; for example, 1/3 = 3/9.
byjus.com/maths/equivalence-relation/The equivalence relationships can be explained in terms of the following examples:
- The symbol of ‘is equal to (=)’ on a set of numbers/ characters/ symbols.
- For example: 1/4 = 2/8
testbook.com/maths/equivalence-relation - People also ask
Equivalence Relations: Definition, Proof, Properties, Examples
WEBNov 9, 2023 · Define Equivalence Relation. An equivalence relation is a binary relation on a set that satisfies three properties: reflexivity, symmetry, and transitivity. It is a way to partition a set into distinct subsets or “ equivalence classes.
See results only from geeksforgeeks.orgEquivalence Class: Definitio…
An equivalence relation is a relation that satisfies three properties: reflexivity, …
Equivalence Relation - Definition, Proof, Properties, Examples
WEBAn 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 …
Equivalence Relation (Definition, Proof & Examples) - BYJU'S
WEBAn equivalence relation is a relation if the relation R is reflexive, symmetric and transitive for a set. Click here to get the equivalence relation proofs and solved examples.
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7.2: Equivalence Relations - Mathematics LibreTexts
WEBApr 17, 2022 · Definition: equivalence relation. Let \(A\) be a nonempty set. A relation \(\sim\) on the set \(A\) is an equivalence relation provided that \(\sim\) is reflexive, …
Equivalence relation - Wikipedia
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive). If , then (symmetric). If and , then (transitive).
Wikipedia · Text under CC-BY-SA licenseEquivalence relations (article) | Khan Academy
WEBAn equivalence relation defines how we can cut up our pie (how we partition our set of values) into slices (equivalence classes). In general, equivalence relations must have …
6.3: Equivalence Relations and Partitions
WEBDefine the relation \(\sim\) on \(\mathbb{Q}\) by \[x\sim y \,\Leftrightarrow\, 2(x-y)\in\mathbb{Z}.\] \(\sim\) is an equivalence relation. Describe the equivalence classes \([0]\) and \(\big[\frac{1}{4}\big]\).
6.3: Equivalence Relations - Mathematics LibreTexts
WEBDefinition: Equivalence Relation. A relation \(\text{R}\) on a set \(S\) is an equivalence relation iff \(\text{R}\) is reflexive, symmetric and transitive.
WEBExample 1. Let f : X ! Y be a function. We can de ne a relation R by R(x; y) (f(x) = y). Example 2. Let X = Y = Z. We can de ne a relation R by R(a; b) ajb. There are many …
Equivalence Relations
WEB5.4 Equivalence Relations. 🔗. In many area of mathematics we care about how mathematical objects relate to each other. In Section 5.3 we used function to relate …
WEBEquivalence relations are a very general mechanism for identifying certain elements in a set to form a new set. Let X be a set. A relation R is just a subset of X X. Choose some …
5.1 Equivalence Relations - Whitman College
WEBMay 1, 2011 · If a, b ∈ A a, b ∈ A, define a ∼ b a ∼ b to mean that a a and b b have the same number of letters; ∼ ∼ is an equivalence relation. . Example 5.1.4 Let A A be the …
Equivalence Relation - Meaning, Examples and Solved Examples …
WEB4 days ago · Solved Examples of Equivalence Relation. 1. Let us consider that F is a relation on the set R real numbers that are defined by xFy on a condition if x-y is an …
1.4: Equivalence Relations - Mathematics LibreTexts
WEBOct 10, 2021 · A relation is called an equivalence relation if it is reflexive, symmetric, and transitive. Given an equivalence relation on \(X\) and an element \(x\in X\text{,}\) we …
Equivalence Relations - University of Alaska system
WEB4.3 Equivalence Relations. 🔗. With modulo arithmetic any number that is equivalent to another can be substituted in arithmetic without changing the result. In an error …
WEBDefinition. An equivalence relation on a set X is a relation ∼ on X such that: x ∼ x for all x ∈ X. (The relation is reflexive.) If x ∼ y, then y ∼ x. (The relation is symmetric.) 3. If x ∼ …
Equivalence Relation | Definition & Examples - Lesson | Study.com
WEBNov 21, 2023 · What is equivalence relation with example? An equivalence relation is a relation that is symmetric, transitive, and reflexive. As an example of an equivalence …
2.2: Equivalence Relations, and Partial order
WEBMay 27, 2022 · Definition: Equivalence Class. Given an equivalence relation \( R \) over a set \( S, \) for any \(a \in S \) the equivalence class of a is the set \( [a]_R =\{ b \in S \mid …
Equivalence Relations - Millersville University of Pennsylvania
WEBDefinition. An equivalence relation on a set X is a relation on X such that: 1. for all . (The relation is reflexive .) 2. If , then . (The relation is symmetric. 3. If and , then . (The …
Equivalence Class: Definition, Properties, and Examples
WEBDec 29, 2023 · An equivalence relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity. Equivalence classes partition the set S into …
7.3: Equivalence Relations - Mathematics LibreTexts
WEBA 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.
Equivalence relations Definition & Meaning - Merriam-Webster
WEBnoun. : a relation (such as equality) between elements of a set (such as the real numbers) that is symmetric, reflexive, and transitive and for any two elements either holds or does …
7.3: Equivalence Classes - Mathematics LibreTexts
WEBApr 17, 2022 · Define a relation \(\sim\) on \(A\) as follows: For \(x, y \in A\), \(x \sim y\) if and only if there exists a set \(U\) in \(\mathcal{C}\) such that \(x \in U\) and \(y \in U\). (b) …
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