4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an equivalence relation. (b) Identify the equivalence classes.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...
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4. For (1, yı) and (r2,y2) in R² we set
(11. yı) ~ (12. Y2) →{+ =3+ yi.
(a) Show that ~ defines an equivalence relation.
(b) Identify the equivalence classes.
Transcribed Image Text:4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an equivalence relation. (b) Identify the equivalence classes.
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