6. Consider the set R2 and relation~: (1, 1)~ (2, 2) if and only if x2 = ₁ + m and y2 = ₁ +n for some m, n € Z. (1) Is an equivalence relation on R2 or not? If so, please verify. If not, please explain why. (2) If your answer is yes for (1), write down the equivalence classes. (3) If your answer is yes for (1), write down the quotient set, and denote it by R2/~ (4) If your answer is yes for (1), draw a picture of R2 and R2/~.

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