Let R be a relation on ℤ given by xRy if and only if x²-y² is divisible by 3. Show that this relation is an equivalence relation and find its corresponding equivalence classes.
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First we show that given relation R is an equivalence relation:
Hence by definition it is indeed an equivalence relation.
Now we find the equivalence classes:
We can see from here, that for every the corresponding equivalence class is: