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An equivalence relation r on a set U is a relation that is symmetric (A r Bimplies B r A), reflexive (Ar A) and transitive (A rB and B r C implies Ar C). If these three properties are true for all elements A, B, and C in U, then r is a equivalence relation on U.

For example, let U be the set of people that live in exactly 1 house. Let r be the relation on Usuch that A r B means that persons A and B live in the same house. Then ris symmetric since if A lives in the same house as B, then B lives in the same house as A. It is reflexive since A lives in the same house as him or herself. It is transitive, since if A lives in the same house as B, and B lives in the same house as C, then Alives in the same house as C. So among people who live in exactly one house, living together is an equivalence relation.

The most well known equivalence relation is the familiar "equals" relationship.

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Q: What are equivalence relations?

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First, let's define an equivalence relation. An equivalence relation R is a collection of elements with a binary relation that satisfies this property:Reflexivity: ∀a ∈ R, a ~ aSymmetry: ∀a, b ∈ R, if a ~ b, then b ~ aTransitivity: ∀a, b, c ∈ R, if a ~ b and b ~ c, then a ~ c.

1 (US) Gallon=3.78541 Litres

Yes. Functions are always relations, but relations are not always functions.

fractions equivalence simplification

Function is a special case of relation. It means function is a relation but all relations are not functions. Therefore all functions are relations.

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The reflexive property, which is a property of all equivalence relations. Two other properties, besides reflexivity, of equivalence relations are: symmetry and transitivity.

I guess you mean to ask:'x = x exemplifies what property of the relation of equality?'.If so, then the answer is:The reflexive property, which is a property of all equivalence relations.Two other properties, besides reflexivity, of equivalence relations are:symmetry and transitivity.

Murray Sidman has written: 'Equivalence relations and behavior' -- subject(s): Behavioral assessment, Behaviorism (Psychology), Equivalence (Linguistics), Experimental Psychology, Research 'Coercion and its fallout' -- subject(s): Avoidance (Psychology), Control (Psychology), Punishment, Reinforcement (Psychology), Social control

It mean the equivalence ratio is equal to 1.

An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.

An equivalence relationship is a relationship over the set of integers defined for as follows:For equivalence modulo n (n being a positive integer),a ~ b (mod n) n divides (a-b)This partitions the set of integers into n equivalence classes: {0, 1, 2, ... , n-1}.

No. The equivalence point is reached when the moles of titrant equals the moles of analyte.

Equivalence capacitance for system of two capacitors in parallel circuit is Ce = C1 + C2 Equivalence capacitance for system of two capacitors in serial circuit is 1/Ce = 1/C1 + 1/C2

An equivalence relation ~ on A partitions into pairwise disjoint subsets called equivalence classes so that 1. Within each class, every pair relates 2. Between classes there is no relation i.e. [x] = {a (element) A | a~x} and given two equivalence classes [a] and [b], either [a] = [b] or [a] intersect [b] = the empty set

pH = 5.56 at 36.0 ml(equivalence point)

it depends on the strength of the acid and base used: so, strong acid + strong base = neutral equivalence point strong acid + weak base = acidic equivalence point weak acid + strong base = basic equivalence point In this case, HCl is a strong acid, and Na2CO3 a weak base. Therefore, the equivalence point will be slightly acidic.