Let R be the equivalence relation defined on Z by x Ry if x ² = y ² (Mod5). Give a partition on Z with respect to R.

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2² = 0 (mod 5) r² = 1 (mod 5) r² = 4 (mod 5) if and only if if and only if if and only if x = 0 (mod 5), x = 1 (mod 5) or I x = 2 (mod 5) or x = 4 (mod 5), x = 3 (mod 5). ) 2² = 0 (mod 5) r² = 1 (mod 5) r² = 4 (mod 5) if and only if if and only if if and only if x = 0 (mod 5), x = 1 (mod 5) or I x = 2 (mod 5) or x = 4 (mod 5), x = 3 (mod 5). )

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