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Problem 1. Let ~ be an equivalence relation on a set S. 1.1. Let a € S, and suppose b€ S is a representative of [a]. Show that [a] = [b]. 1.2. Let a, b = S and suppose [a] = [b]. Show that [a] and [b] do not intersect: [a][b]=0.

Problem 1. Let ~ be an equivalence relation on a set S. 1.1. Let a € S, and suppose b€ S is a representative of [a]. Show that [a] = [b]. 1.2. Let a, b = S and suppose [a] = [b]. Show that [a] and [b] do not intersect: [a][b]=0.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.6: Relations
Problem 44PFA
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Problem 1. Let ~ be an equivalence relation on a set S. 1.1. Let a € S, and suppose b€ S is a representative of [a]. Show that [a] = [b]. 1.2. Let a, b = S and suppose [a] = [b]. Show that [a] and [b] do not intersect: [a][b]=0.
Transcribed Image Text:Problem 1. Let ~ be an equivalence relation on a set S. 1.1. Let a € S, and suppose b€ S is a representative of [a]. Show that [a] = [b]. 1.2. Let a, b = S and suppose [a] = [b]. Show that [a] and [b] do not intersect: [a][b]=0.
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