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2 Relations For the following relation R over the integers, prove whether R is or is not: 1. Reflexive, 2. Anti-reflexive, 3. Symmetric, 4. Anti-symmetric, 5. Transitive, 6. Partial Order, 7. Strict Order, 8. Equivalence relation = ky} a) R = {(x,y) EZ² : 3 KEZX =

2 Relations For the following relation R over the integers, prove whether R is or is not: 1. Reflexive, 2. Anti-reflexive, 3. Symmetric, 4. Anti-symmetric, 5. Transitive, 6. Partial Order, 7. Strict Order, 8. Equivalence relation = ky} a) R = {(x,y) EZ² : 3 KEZX =

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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2 Relations For the following relation R over the integers, prove whether R is or is not: 1. Reflexive, 2. Anti-reflexive, 3. Symmetric, 4. Anti-symmetric, 5. Transitive, 6. Partial Order, 7. Strict Order, 8. Equivalence relation a) R = {(x,y) EZ² : 3 kezx = ky}
Transcribed Image Text:2 Relations For the following relation R over the integers, prove whether R is or is not: 1. Reflexive, 2. Anti-reflexive, 3. Symmetric, 4. Anti-symmetric, 5. Transitive, 6. Partial Order, 7. Strict Order, 8. Equivalence relation a) R = {(x,y) EZ² : 3 kezx = ky}
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