The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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HW#9

In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive; it
is therefore an equivalence relation; (4) sketch it, by drawing the underlying set as a subset of the
plane, then colouring each equivalence class in a different colour.
Transcribed Image Text:In problems 4, 5: show that the relation described is (1) reflexive, (2) symmetric, (3) transitive; it is therefore an equivalence relation; (4) sketch it, by drawing the underlying set as a subset of the plane, then colouring each equivalence class in a different colour.
5. The relation
on Z x N defined by, (a, b) ~ (c, d) if ad = bc.
bc.
Transcribed Image Text:5. The relation on Z x N defined by, (a, b) ~ (c, d) if ad = bc. bc.
Expert Solution
Step 1

The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation.

To show that any relation is equivalent then,

It is enough to show that

(1) reflexive

(2) transitive

(3) symmetric

The reflection is symmetric since,

a,a~(a,a) then a2=a2

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