what is meant by equivalent class
Asked by banga71 | 7th Apr, 2017, 10:05: PM
Expert Answer:
An equivalence class is defined as a subset of the form
,
where a is an element of
and R is the equivalence relation between
and
.
Note that any two equivalence classes can either be either equal or disjoint,
Hence, the collection of equivalence classes forms a partition of
.
Example:
Consider the set,
S ={0,1,2,3,4,5}
There are many equivalence relations we could define on this set.
One would be xRy iff x=y,
in which case the equivalence classes are:
[0]={0}
[1]={1}
.
.
.
.
.
[5]={5}
We could also define xRy iff x≡y(mod3), in which case our equivalence classes are:
[0]=[3]={0,3}
[1]=[4]={1,4}
[2]=[5]={2,5}





Consider the set, S ={0,1,2,3,4,5}
There are many equivalence relations we could define on this set.
One would be xRy iff x=y,
in which case the equivalence classes are:
[0]={0}
[1]={1}
.
.
.
.
.
[5]={5}
We could also define xRy iff x≡y(mod3), in which case our equivalence classes are:
[0]=[3]={0,3}
[1]=[4]={1,4}
[2]=[5]={2,5}
|
Answered by Rebecca Fernandes | 27th Nov, 2017, 02:36: PM
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