In 43, 44, 45, 46, 47, 48, 49, and 50, the following definitions are used: A relation on a set A is defined to be irreflexive if, and only if, for every x € A‚ x K x; asymmetric if, and only if, for every x, y ≤ A if x Ry then y Kx; intransitive if, and only if, for every x, y, z € A, if x R y and y R z then x K z. For each of the relations in the referenced exercise, determine whether the relation is irreflexive, asymmetric, intransitive, or none of these. 43. R₁ = {(0,0), (0, 1), (0, 3), (1, 1), (1, 0), (2, 3), (3, 3)} Answer 44. R₂ = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} 45. R3 = {(2, 3), (3, 2)} Answer 46. R4 = {(1, 2), (2, 1), (1, 3), (3, 1)} 47. R5 = {(0,0), (0, 1), (0, 2), (1, 2)} 48. R6 = {(0, 1), (0, 2)}

In 43, 44, 45, 46, 47, 48, 49, and 50, the following definitions are used: A relation on a set A is defined to be irreflexive if, and only if, for every x € A‚ x K x; asymmetric if, and only if, for every x, y ≤ A if x Ry then y Kx; intransitive if, and only if, for every x, y, z € A, if x R y and y R z then x K z. For each of the relations in the referenced exercise, determine whether the relation is irreflexive, asymmetric, intransitive, or none of these. 43. R₁ = {(0,0), (0, 1), (0, 3), (1, 1), (1, 0), (2, 3), (3, 3)} Answer 44. R₂ = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} 45. R3 = {(2, 3), (3, 2)} Answer 46. R4 = {(1, 2), (2, 1), (1, 3), (3, 1)} 47. R5 = {(0,0), (0, 1), (0, 2), (1, 2)} 48. R6 = {(0, 1), (0, 2)}

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....

See similar textbooks