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1, let m be an integer with m> 1. Define the relation R on the set of integers where aRb if a = b mod m if there exists an integer k such that mk = a - b that is, m divides a - b. show that this relation is an equivalence relation by showing that it is reflective, symmetric, and transitive A show that this relation is reflective. B, show that this relation is symmetric. C, show that this relation is transitive

1, let m be an integer with m> 1. Define the relation R on the set of integers where aRb if a = b mod m if there exists an integer k such that mk = a - b that is, m divides a - b. show that this relation is an equivalence relation by showing that it is reflective, symmetric, and transitive A show that this relation is reflective. B, show that this relation is symmetric. C, show that this relation is transitive

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1, let m be an integer with m > 1. Define the relation R on the set of integers where aRb if a = b mod m if there exists an integer k such that mk = a - b that is, m divides a - b. show that this relation is an equivalence relation by showing that it is reflective, symmetric, and transitive A show that this relation is reflective. B, show that this relation is symmetric. C, show that this relation is transitive
Transcribed Image Text:1, let m be an integer with m > 1. Define the relation R on the set of integers where aRb if a = b mod m if there exists an integer k such that mk = a - b that is, m divides a - b. show that this relation is an equivalence relation by showing that it is reflective, symmetric, and transitive A show that this relation is reflective. B, show that this relation is symmetric. C, show that this relation is transitive
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