Let A = {1, 2, 3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and [4] has only one member. Determine the equivalence classes of R.

Let A = {1, 2, 3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and [4] has only one member. Determine the equivalence classes of R.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 4TFE: Label each of the following statements as either true or false. If R is an equivalence relation on a...

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Question

Let A = {1, 2, 3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2,
3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and
[4] has only one member. Determine the equivalence classes of R.

Let A = {1,2,3, 4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2,
а.
3R5 and 6R3. Also assume R has 3 equivalence classes, no equivalence class has 4 members, and
[4] has only one member. Determine the equivalence classes of R. (Hint: it may help to draw the
digraph representation of R.)

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