Question
Let R be the equivalence relation defined on Z by x Ry if x 2 = y 2 (Mod5). Give a partition on Z with
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.
(you may use the following results:
2 = 0 (mod 5) r = 1 (mod 5) r = 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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Linear Algebra and Its Applications
Authors: David C. Lay
4th edition
321791541, 978-0321388834, 978-0321791542
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