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Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and define a relation R on A as follows: For all x, y EA, x Ry3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] = [1] = [2] = [3] = { -6, - 5. - 4, – 3, - 2, - 1,0,1,2,3} {−6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} {-6, - 5.-4, -3, -2,-1,0,1,2,3} {−6, – 5. — 4, – 3, — 2, – 1,0,1,2,3} - X X X How many distinct equivalence classes does R have? 1 X classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and define a relation R on A as follows: For all x, y EA, x Ry3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] = [1] = [2] = [3] = { -6, - 5. - 4, – 3, - 2, - 1,0,1,2,3} {−6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} {-6, - 5.-4, -3, -2,-1,0,1,2,3} {−6, – 5. — 4, – 3, — 2, – 1,0,1,2,3} - X X X How many distinct equivalence classes does R have? 1 X classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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1. [0/1 Points] [0] = [1] = Let A = {-6, -5, −4, −3,−2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all x, y EA, x Ry⇒ 3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [2] = DETAILS [3] = PREVIOUS ANSWERS { −6, — 5. — 4, — 3, -2, - 1,0,1,2,3} {−6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} - - { −6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} { −6, — 5. — 4, — 3, -2, -1,0,1,2,3} EPPDISCMATH5 8.3.006. X How many distinct equivalence classes does R have? 1 X classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
Transcribed Image Text:1. [0/1 Points] [0] = [1] = Let A = {-6, -5, −4, −3,−2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all x, y EA, x Ry⇒ 3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [2] = DETAILS [3] = PREVIOUS ANSWERS { −6, — 5. — 4, — 3, -2, - 1,0,1,2,3} {−6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} - - { −6, — 5. — 4, — 3, — 2, — 1,0,1,2,3} { −6, — 5. — 4, — 3, -2, -1,0,1,2,3} EPPDISCMATH5 8.3.006. X How many distinct equivalence classes does R have? 1 X classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
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