Homework Help is Here – Start Your Trial Now!
Math
Algebra
1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x² – y² is even number . Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.

1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x² – y² is even number . Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.

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 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
See similar textbooks
icon
Related questions
Question
100%
1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x² – y² is even number . Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.
Transcribed Image Text:1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x² – y² is even number . Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer