Equivalence ClassesLet R be defined on Z x Z where z Ry if æ = y( mod 7)Define the equivalence classes of R as P = {[0], [1], [2], [3], [4], [5], [6]} where the equivalence class isthe remainder mod 7.a) Determine if (12, 1083) E R. Justify your answer.b) Find a member, x of each of the 7 equivalence classes where a > 100.

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Answered: Let R be defined on Z x Z where a R y…

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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Let m ∈ Z, m ≠ 0. Congruence modulo m is an equivalence relation: (a) For all a ∈ Z, a ≡ a mod m (Reflextivity) (b) For all a,b ∈ Z, if a ≡ b mod m, then b ≡ a mod m. (Symmetry) (c) For all a,b, c ∈ Z, if a ≡ b mod m and b ≡ c mod m, then a ≡ c mod m. (Transitivity)
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The congruence class of [6], is {...-9,4,1,6, – 11...} {...-9,-4,–1,6,11...} {...-9,-4,1,6,11...} {...-9,-4,1,5,11..}
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