solve these two questions 14. Show that the relation defined on Z as follows are equivalence relation(a) For all, n e Z, m R n <=> 3|(m² — n²).(b) Let A = Z+ × Z+, define a binary relation R on A:(a, b) R (c,d) <=> a+d=c+ b for all (a, b) and (c,d) in A.15. Prove that(a) If A is a set, R is an equivalence relation on A, then distinct equivalence classes ofR form a partition of A; that is, the union of the equivalence classes is all of A, andthe intersection of any two distinct classes is empty...and a and b are elements of A,(b) If A is a set, R is an equivalent relation on A, and a and b are elements of A, Theneither [a] n [b] = Ø or [a] = [b].

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Answered: 4. Show that the relation defined on Z…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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4. Show that the relation defined on Z as follows are equivalence relation (a) For all, n € Z, m R n <=> 3|(m² – n²). (b) Let A = : Z+ × Z+, define a binary relation R on A: (a, b) R (c,d) <=> a+d=c+ b for all (a, b) and (c,d) in A.