Question

Give detailed Conception of : Equivalence Relation

Answer 1

@abhi_abhi

Answer 2

@wio @waterineyes

Answer 3

An equivalence relation is a relation (funnily enough) that satisfies these three properties...
Reflexivity
a ~ a
Symmetry
If a~b then b~a
Transitivity
If a~b and b~c, then a~c

Basically a generalisation of the relation of equality, you'll find that equality is an equivalence relation :)

Answer 4

Equivalence Relation
An equivalence relation on a set X is a subset ofXxX , i.e., a collection R of ordered pairs of elements of X, satisfying certain properties.
Write "xRy" to mean(x,y) is an element of R , and we say " x is related to y," then the properties are

1. Reflexive: aRa for all \[a \in R\] ,

2. Symmetric: aRb implies bRa for all \[a,b \in R\]

3. Transitive: aRb and bRc imply aRc for all \[a,b,c \in R\],
where these three properties are completely independent. Other notations are often used to indicate a relation
e.g.,a~b