3. Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(f, g) | f(1) = g(1)} b) {(f, g) | f(0) = g(0) or f(1) = g(1)} c) {(f, g) | f(x) – g(x) = 1 for all x EZ} d) (f. g)| for some CEZ, for all x E Z, f(x) – %3D g(x) = C} e) {f, g) | f(0) = g(1) and f(1) = g(0)} %3D

3. Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(f, g) | f(1) = g(1)} b) {(f, g) | f(0) = g(0) or f(1) = g(1)} c) {(f, g) | f(x) – g(x) = 1 for all x EZ} d) (f. g)| for some CEZ, for all x E Z, f(x) – %3D g(x) = C} e) {f, g) | f(0) = g(1) and f(1) = g(0)} %3D

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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Similar questions

please answer number 7. If you can please answer as much as you can.
NOTE: This question requires that I find the equivalence classes and not the equivalence relations.
i need the answer quickly
Discrete math: please solve both parts 100% accurate
please send handwritten solution for part b
2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a, b) = (a₁, b₁) if a = a₁. (d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.