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Let R be defined on Z x Z where a R y if æ = y( mod 7) Define the equivalence classes of R as P = {[0], [1], [2], [3], [4], [5], [6]} where the equivalence class is the remainder mod 7. a) Determine if (12, 1083) e R. Justify your answer. b) Find a member, æ of each of the 7 equivalence classes where a > 100.

Let R be defined on Z x Z where a R y if æ = y( mod 7) Define the equivalence classes of R as P = {[0], [1], [2], [3], [4], [5], [6]} where the equivalence class is the remainder mod 7. a) Determine if (12, 1083) e R. Justify your answer. b) Find a member, æ of each of the 7 equivalence classes where a > 100.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 5E: 5. Let be the relation “congruence modulo ” defined on as follows: is congruent to modulo if...
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Equivalence Classes Let R be defined on Z x Z where z Ry if æ = y( mod 7) Define the equivalence classes of R as P = {[0], [1], [2], [3], [4], [5], [6]} where the equivalence class is the remainder mod 7. a) Determine if (12, 1083) E R. Justify your answer. b) Find a member, x of each of the 7 equivalence classes where a > 100.
Transcribed Image Text:Equivalence Classes Let R be defined on Z x Z where z Ry if æ = y( mod 7) Define the equivalence classes of R as P = {[0], [1], [2], [3], [4], [5], [6]} where the equivalence class is the remainder mod 7. a) Determine if (12, 1083) E R. Justify your answer. b) Find a member, x of each of the 7 equivalence classes where a > 100.
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