Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows:R = {(0, 1), (1,1), (2, 3),(3,3)}S= {(0, 0), (0, 2), (0, 3), (2, 3)},T = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (1, 3),(2, 2), (3, 0), (3, 3)},%3DT has . propertiesSeç.Seç.The equivalance relation is:RS has . propertiestransitive, symmetric but not reflexivereflexive, symmetric but not transitiveR has . propertiesreflexive, symmetric and transitivereflexive, but neither symmetric nor transitivereflexive, transitive but not symmetrictransitive, but neither symmetric nor reflexivesymmetric, but neither reflexive nor transitive

Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows R = {(0, 1), (1,1), (2, 3),(3,3)} S= {(0, 0), (0, 2), (0, 3), (2, 3)}, T = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (1, 3),(2, 2), (3, 0), (3, 3)}, T has . properties Seç. The equivalance relation is: Seç..

Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows R = {(0, 1), (1,1), (2, 3),(3,3)} S= {(0, 0), (0, 2), (0, 3), (2, 3)}, T = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (1, 3),(2, 2), (3, 0), (3, 3)}, T has . properties Seç. The equivalance relation is: Seç..

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 1E: Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary...

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Question

Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows:
R = {(0, 1), (1,1), (2, 3),(3,3)}
S= {(0, 0), (0, 2), (0, 3), (2, 3)},
T = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (1, 3),(2, 2), (3, 0), (3, 3)},
%3D
T has . properties
Seç.
Seç.
The equivalance relation is:
R
S has . properties
transitive, symmetric but not reflexive
reflexive, symmetric but not transitive
R has . properties
reflexive, symmetric and transitive
reflexive, but neither symmetric nor transitive
reflexive, transitive but not symmetric
transitive, but neither symmetric nor reflexive
symmetric, but neither reflexive nor transitive

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