Let R be the relation on the set of real numbers such that x R y if and only if x and y are real numbers that differ by less than 1, that is | x – y | < 1. Determine whether R is reflexive, symmetric and transitive.
Let R be the relation on the set of real numbers such that x R y if and only if x and y are real numbers that differ by less than 1, that is | x – y | < 1. Determine whether R is reflexive, symmetric and transitive.
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 R be the relation on the set of real numbers such that x R y if
and only if x and y are real numbers that differ by less than 1, that
is | x – y | < 1. Determine whether R is reflexive, symmetric and
transitive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7ae680f-bd19-413f-899e-d28712f6b138%2Fab91b4b1-bb86-4d75-b6da-b8b0b0b6507f%2Fbidyftn_processed.png&w=3840&q=75)
Transcribed Image Text:Let R be the relation on the set of real numbers such that x R y if
and only if x and y are real numbers that differ by less than 1, that
is | x – y | < 1. Determine whether R is reflexive, symmetric and
transitive.
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