Let ∼ be the relation on Z defined as follows: For every m, n ∈ Z,m ∼ n ⇐⇒ 5|(m 2 − n 2 ).We proved previously that ∼ is an equivalence relation.(a) Show that a ∼ −a for all a ∈ Z.(b) Show that if a ≡ b (mod 5), then a ∼ b.(c) Find the equivalence classes of ∼, justifying your answer. Use the results from parts (a) and (b). (a) Show that a ~ -a for all a € Z.(b) Show that if a = b (mod 5), then a ~ b.(c) Find the equivalence classes of~, justifying your answer. Let~be the relation on Z defined as follows: For every m, n = Z,5/(m²-n²).M~ n

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Answered: Let ~ be the relation on Z defined as…

Math

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Let ~ be the relation on Z defined as follows: For every m, n = Z, 5/(m²-n²). M~ n

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let ∼ be the relation on Z defined as follows: For every m, n ∈ Z,

m ∼ n ⇐⇒ 5|(m 2 − n 2 ).

We proved previously that ∼ is an equivalence relation.

(a) Show that a ∼ −a for all a ∈ Z.

(b) Show that if a ≡ b (mod 5), then a ∼ b.

Let
~
be the relation on Z defined as follows: For every m, n = Z,
5/(m²-n²).
M~ n

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