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1. xy iff x-y is divisible by 3. (Note: 0 is considered to be divisible by 3.). HINT: Compare this problem to an example from lecture 10, recalling that by definition, an even integer is an integer which is divisible by 2. SS0S T 880 TAMA 2. xy iff x - y = 1, ATOWSINOH 3. xy iff xy ≥ 0.

1. xy iff x-y is divisible by 3. (Note: 0 is considered to be divisible by 3.). HINT: Compare this problem to an example from lecture 10, recalling that by definition, an even integer is an integer which is divisible by 2. SS0S T 880 TAMA 2. xy iff x - y = 1, ATOWSINOH 3. xy iff xy ≥ 0.

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 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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1. xy iff x-y is divisible by 3. (Note: 0 is considered to be divisible by 3.). HINT: Compare this problem to an example from lecture 10, recalling that by definition, an even integer is an integer which is divisible by 2. 2. x~y iff x - y = 1, TOWSINOH SS0S IT 888 TAMA 3. x~y iff xy ≥ 0. 4. xy iff x = y or x = -y.vebonbonCh
Transcribed Image Text:1. xy iff x-y is divisible by 3. (Note: 0 is considered to be divisible by 3.). HINT: Compare this problem to an example from lecture 10, recalling that by definition, an even integer is an integer which is divisible by 2. 2. x~y iff x - y = 1, TOWSINOH SS0S IT 888 TAMA 3. x~y iff xy ≥ 0. 4. xy iff x = y or x = -y.vebonbonCh
Problem 7. Which of the following relations ~on Z is an equivalence relation? Explain your answer, and for each relation that is an equivalence relation, give the set Z/~ of all equivalence classes. 1
Transcribed Image Text:Problem 7. Which of the following relations ~on Z is an equivalence relation? Explain your answer, and for each relation that is an equivalence relation, give the set Z/~ of all equivalence classes. 1
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