Exercise A.1.5. Define~ on S = {(a,b): a,b E Z,b 0} by (a, b) ~ (c, d) if and only if ad – bc = 0.(1) Show~ is an equivalence relation on S.(2) Describe the equivalence classes of ~.(3) Describe the quotient S/ ~. What familiar set does this look like?

Given: Define ~ on S=a, b: a, b∈ℤ, b≠0 by a, b~c, d if and only if ad-bc=0. To show: 1) ~ is an…

Answered: (1) Show v is an equivalence relation…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...

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(1) Show v is an equivalence relation on S. (2) Describe the equivalence classes of . (3) Describe the quotient S/ • ~. What familiar set does this look like?