Consider the following binary set relation: R= {(1,5), (2, 2), (5, 1)}, on A = {1, 2, 5} a) Compute its transitive closure, R+ b) Prove or disprove: U{R+, AA} is an equivalence relation

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 10E: In Exercises , a relation is defined on the set of all integers. In each case, prove that is an...
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Consider the following binary set relation:
R = {(1,5), (2, 2), (5, 1)}, on A = {1, 2, 5}
a) Compute its transitive closure, R+
b) Prove or disprove: U{R+, AA} is an equivalence relation
c) Prove or disprove: FOR ALL relations P on set B with transitive closure
Pt, U{P+,AB} is an equivalence relation
Transcribed Image Text:Consider the following binary set relation: R = {(1,5), (2, 2), (5, 1)}, on A = {1, 2, 5} a) Compute its transitive closure, R+ b) Prove or disprove: U{R+, AA} is an equivalence relation c) Prove or disprove: FOR ALL relations P on set B with transitive closure Pt, U{P+,AB} is an equivalence relation
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