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A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x; asymmetric if, and only if, for every x, y E A if x R y then y R x; intransitive if, and only if, for every x, y, z E A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R, on A as follows. 2 R, = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) OR, is irreflexive. R2 is asymmetric. is intransitive. OR, is neither irreflexive, asymmetric, nor intransitive. Need Help? Read It

A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x; asymmetric if, and only if, for every x, y E A if x R y then y R x; intransitive if, and only if, for every x, y, z E A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R, on A as follows. 2 R, = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) OR, is irreflexive. R2 is asymmetric. is intransitive. OR, is neither irreflexive, asymmetric, nor intransitive. Need Help? Read It

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 21E: 21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in...
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A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x; asymmetric if, and only if, for every x, y E A if x R y then y R x; intransitive if, and only if, for every x, y, z E A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R, on A as follows. 2 R, = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) OR, is irreflexive. R2 is asymmetric. is intransitive. OR, is neither irreflexive, asymmetric, nor intransitive. Need Help? Read It
Transcribed Image Text:A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x; asymmetric if, and only if, for every x, y E A if x R y then y R x; intransitive if, and only if, for every x, y, z E A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R, on A as follows. 2 R, = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) OR, is irreflexive. R2 is asymmetric. is intransitive. OR, is neither irreflexive, asymmetric, nor intransitive. Need Help? Read It
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