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 {x in X:xRa},
where a is an element of X and R is the equivalence relation between x and y.
Note that any two equivalence classes can either be either equal or disjoint,
Hence, the collection of equivalence classes forms a partition of X.
 
Example:
 

Consider the set,

={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 xy(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