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Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an equivalence relation on Z. 2. Determine all the equivalence classes under = 3. How many are there? 3. Verify that equivalence classes form a partition on Z.

Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an equivalence relation on Z. 2. Determine all the equivalence classes under = 3. How many are there? 3. Verify that equivalence classes form a partition on Z.

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 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...
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Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an equivalence relation on Z. 2. Determine all the equivalence classes under = 3. How many are there? 3. Verify that equivalence classes form a partition on Z.
Transcribed Image Text:Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an equivalence relation on Z. 2. Determine all the equivalence classes under = 3. How many are there? 3. Verify that equivalence classes form a partition on Z.
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