Let R be an equivalence relation on A = {0, 1,5, 6, 8, 9} andR = {(6, 1), (1,6), (6, 6), (1, 1), (0, 0), (5, 5), (5, 8), (5,9), (8,5), (8, 8), (8, 9), (9, 5), (9, 8), (9,9)}.Show the partition of A defined by the equivalence classes of R.

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Answered: Let R be an equivalence relation on A =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
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1. Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: ! = {(1,1), (2, 2), (3, 3), (4, 4), (5,5), (6,6), (2, 3), (3,2), (4, 5), (5, 4), (4, 6), (6,4), (5, 6), (6,5)}. R = List the equivalence classes of R. 2. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence classes. Also aRd, bRc and eRd. Write out R as a set. 3. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has three equivalence classes. Also aRd and bRc. Write out R as a set. 4. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose also that aRd and bRc, eRa and cRe. How many equivalence classes does R have? 5. There are two different equivalence relations on the set A = {a, b}. Describe them. Diagrams will suffice. 6. There are five different equivalence relations on the set A = {a,b,c}. Describe them all. Diagrams will suffice. 7. Define a relation R on Z as xRy if and only if 3x-5y is even. Prove R is an equivalence…

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Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1), (0, 0), (5, 5), (5, 8), (5,9), (8, 5), (8, 8), (8, 9), (9, 5), (9, 8), (9,9)}. Show the partition of A defined by the equivalence classes of R.