4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) E Z x Z[ m = {(n,m) E Z x Z| (n is even A m is odd) V (n is odd A m is even)}. = {(n,m) E Z x Z| m = 100}. b. R= - -n}.
4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) E Z x Z[ m = {(n,m) E Z x Z| (n is even A m is odd) V (n is odd A m is even)}. = {(n,m) E Z x Z| m = 100}. b. R= - -n}.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 2E: 2. In each of the following parts, a relation is defined on the set of all integers. Determine in...
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Transcribed Image Text:4.
Consider the following relations R on the integers Z. For each of these relations, say
whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a
function; (iv) R is irreflexive.
a. R= {(n, m) EZ x Z| m =
100}.
b. R= {(n,m) EZ x Z| (n is even A m is odd) V (n is odd A m is even)}.
%3D
c. R= {(n,m) EZ x Z| m = –
= -n}.
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