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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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What is meant by symmetric reflexive and transitive property and also equivalence relation?
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.
How do you equivalence of liters and gallons in fraction form?
1 (US) Gallon=3.78541 Litres
Is a function is always a relation?
Yes. Functions are always relations, but relations are not always functions.
What are the answers to heinemann mathematics p7 link upworkbook pg 34 textbookpg 114?
fractions equivalence simplification
Why all functions relation?
Function is a special case of relation. It means function is a relation but all relations are not functions. Therefore all functions are relations.
