A relation R on a set A is defined to be irreflexive if, and only if, for every x EA, x R x; asymmetric if, and only if, for every x, y E A if x Ry then y R x; intransitive if, and only if, for every x, y, z EA, if x Ry and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R7 on A as follows. R7 = {(0, 3), (2, 3)} Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) ✓ R, is irreflexive. ✓ R7 is asymmetric. ☐ R7 is intransitive. R7 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 EA, x R x; asymmetric if, and only if, for every x, y E A if x Ry then y R x; intransitive if, and only if, for every x, y, z EA, if x Ry and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R7 on A as follows. R7 = {(0, 3), (2, 3)} Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) ✓ R, is irreflexive. ✓ R7 is asymmetric. ☐ R7 is intransitive. R7 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 22E: A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which...
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![A relation R on a set A is defined to be
irreflexive if, and only if, for every x EA, x R x;
asymmetric if, and only if, for every x, y E A if x Ry then y R x;
intransitive if, and only if, for every x, y, z EA, if x Ry and y R z then x R z.
Let A = {0, 1, 2, 3}, and define a relation R7 on A as follows.
R7 = {(0, 3), (2, 3)}
Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.)
✓ R, is irreflexive.
✓ R7 is asymmetric.
☐ R7 is intransitive.
R7
is neither irreflexive, asymmetric, nor intransitive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3cf874b-7a7b-478f-a7b8-421442e72224%2Fcec7dabe-dc44-4a33-8f6a-909116796d69%2Frjivd0d_processed.png&w=3840&q=75)
Transcribed Image Text:A relation R on a set A is defined to be
irreflexive if, and only if, for every x EA, x R x;
asymmetric if, and only if, for every x, y E A if x Ry then y R x;
intransitive if, and only if, for every x, y, z EA, if x Ry and y R z then x R z.
Let A = {0, 1, 2, 3}, and define a relation R7 on A as follows.
R7 = {(0, 3), (2, 3)}
Is R, irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.)
✓ R, is irreflexive.
✓ R7 is asymmetric.
☐ R7 is intransitive.
R7
is neither irreflexive, asymmetric, nor intransitive.
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