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Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by the rule: (a, b) E E if and only if (a, b) E RA (b, a) E R. Prove that E is an equivalence relation on A, that is, prove that E is reflexive, symmetric, and transitive.

Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by the rule: (a, b) E E if and only if (a, b) E RA (b, a) E R. Prove that E is an equivalence relation on A, that is, prove that E is reflexive, symmetric, and transitive.

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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7. Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by the rule: (a, b) E E if and only if (a, b) E RA (b, a) E R. Prove that E is an equivalence relation on A, that is, prove that E is reflexive, symmetric, and transitive.
Transcribed Image Text:7. Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by the rule: (a, b) E E if and only if (a, b) E RA (b, a) E R. Prove that E is an equivalence relation on A, that is, prove that E is reflexive, symmetric, and transitive.
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