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Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3, because 1³-33-1-27= -26, which is 13 times 1-3. Prove that is an equivalence relation. ~

Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3, because 1³-33-1-27= -26, which is 13 times 1-3. Prove that is an equivalence relation. ~

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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Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3, because 1³-33-1-27= -26, which is 13 times 1-3. 7 Prove that is an equivalence relation.
Transcribed Image Text:Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3, because 1³-33-1-27= -26, which is 13 times 1-3. 7 Prove that is an equivalence relation.
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