Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is an equivalence relation. Describe the elements of [(2,3)]. How can we then interpret the equivalence classes in this case?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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Let A = Z and B =Z\{0}. Show that the relation R on A x B defined by (a,b)R(c, d) if ad = bc, is an equivalence relation. Describe the elements
of [(2, 3)]. How can we then interpret the equivalence classes in this case?
Transcribed Image Text:Let A = Z and B =Z\{0}. Show that the relation R on A x B defined by (a,b)R(c, d) if ad = bc, is an equivalence relation. Describe the elements of [(2, 3)]. How can we then interpret the equivalence classes in this case?
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