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1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S, defined by R = {(A, B): A c B}. Show that R is transitive but neither reflexive nor symmetric.

1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S, defined by R = {(A, B): A c B}. Show that R is transitive but neither reflexive nor symmetric.

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 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S, defined by R = {(A, B): A c B}. Show that R is transitive but neither reflexive nor symmetric.
Transcribed Image Text:1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S, defined by R = {(A, B): A c B}. Show that R is transitive but neither reflexive nor symmetric.
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