Let S = {A, B,C,D,E}. a) Give an example of a partition on Sand explain why your example is a partition. b) Consider the equivalence relation induced by your partition. Find two points of this equivalence relation, written in the form xRy. c) Draw the directed graph for your equivalence relation. d) In general, is it possible for the directed graph of an equivalence relation to be disconnected? Isit possible for the directed graph to be simple? Explain.

Let S = {A, B,C,D,E}. a) Give an example of a partition on Sand explain why your example is a partition. b) Consider the equivalence relation induced by your partition. Find two points of this equivalence relation, written in the form xRy. c) Draw the directed graph for your equivalence relation. d) In general, is it possible for the directed graph of an equivalence relation to be disconnected? Isit possible for the directed graph to be simple? Explain.

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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