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Expert Answer
,
and R is the equivalence relation between 
and 
. 
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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}
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