Let S be the following relation on R: S = {(x, y) = R² :y-x is rational}. Prove that S is an equivalence relation.
Let S be the following relation on R: S = {(x, y) = R² :y-x is rational}. Prove that S is an equivalence relation.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.1: Finite Permutation Groups
Problem 33E: Exercises
33. Prove Theorem : Let be a permutation on with . The relation defined on by
if and...
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Let S be the following relation on R:
S = {(x, y) = R² :y-x is rational}.
Prove that S is an equivalence relation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9337f081-cc74-4ca5-9ca3-6c212ee96a0a%2Fb40d9ca0-54aa-4984-bea1-5d0d41819c08%2Foiwcyvr_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 6
Let S be the following relation on R:
S = {(x, y) = R² :y-x is rational}.
Prove that S is an equivalence relation.
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