Recall the equivalence relation defined on Z by mn whenever m - n isdivisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes.Z→ C by g(x) = [x].a. Find g(1), g(-1), and g(18)b. Write the set {x: g(x) = [0]} as a subset of Z.Define g: Z

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Answered: Recall the equivalence relation defined…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let C = {1, 2, 4), A = Cx C, and define a relation on A by: (u, v) R (x, y) if and only if uy = XV. A. Show that R is an equivalence relation on A. Remember that the elements of A are ordered pairs. B. Compute the partition A/R that corresponds to the equivalence relation. Hint: Keep in mind that you are partitioning the 9 elements of A into blocks.
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Recall the equivalence relation defined on Z by mn whenever m - n is divisible by 3. Let C be the set {[0], [1], [2]} of equivalence classes. Z→ C by g(x) = [x]. a. Find g(1), g(-1), and g(18) b. Write the set {x: g(x) = [0]} as a subset of ZZ. Define g: Z