A relation R on a set A is defined to be irreflexive if, and only if, for every x ∈ A, x R x; asymmetric if, and only if, for every x, y ∈ A if x R y then y R x; intransitive if, and only if, for every x, y, z ∈ A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R4 on A as follows. R4 = (1, 2), (2, 1), (1, 3), (3, 1) Is R4 irreflexive, asymmetric, intransitive, or none of these? R4 is irreflexive.R4 is asymmetric.R4 is intransitive.R4 is neither irreflexive, asymmetric, nor intransitive.

A relation R on a set A is defined to be irreflexive if, and only if, for every x ∈ A, x R x; asymmetric if, and only if, for every x, y ∈ A if x R y then y R x; intransitive if, and only if, for every x, y, z ∈ A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R4 on A as follows. R4 = (1, 2), (2, 1), (1, 3), (3, 1) Is R4 irreflexive, asymmetric, intransitive, or none of these? R4 is irreflexive.R4 is asymmetric.R4 is intransitive.R4 is neither irreflexive, asymmetric, nor intransitive.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

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Question

A relation R on a set A is defined to be

irreflexive if, and only if, for every
x ∈ A,
x R x;
asymmetric if, and only if, for every
x, y ∈ A
if
x R y
then y R x;
intransitive if, and only if, for every
x, y,

z ∈ A,
if
x R y
and
y R z
then x R z.

Let

A = {0, 1, 2, 3},

and define a relation

R₄

on A as follows.

R₄ = (1, 2), (2, 1), (1, 3), (3, 1)

R₄

irreflexive, asymmetric, intransitive, or none of these?

R₄ is irreflexive.R₄ is asymmetric.R₄ is intransitive.R₄ is neither irreflexive, asymmetric, nor intransitive.

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