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Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For all x, y € A, TRy if and only if x = y (mod 9). Given that R is an equivalence relation on A, which one of the following sets P is a partition of A into equivalence classes of R? A. P ={{-42}, {-6}, {-7, 11}, {29,-2}, {1}, {10}} B. P ={{-42, -7, -6, -2, 1, 10, 11, 29}} C. P ={{-42, -7,-6}, {-2, 1}, {10, 11,29}} D. P ={{-42,-6}, {-7, 11,29}, {-2}, {1, 10}} E. P ={{-42, -6, -7}, {11,29}, {-2}, {1, 10}} F. P = {{-42,-6}, {11, 29}, {−7, −2}, {1,10}}

Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For all x, y € A, TRy if and only if x = y (mod 9). Given that R is an equivalence relation on A, which one of the following sets P is a partition of A into equivalence classes of R? A. P ={{-42}, {-6}, {-7, 11}, {29,-2}, {1}, {10}} B. P ={{-42, -7, -6, -2, 1, 10, 11, 29}} C. P ={{-42, -7,-6}, {-2, 1}, {10, 11,29}} D. P ={{-42,-6}, {-7, 11,29}, {-2}, {1, 10}} E. P ={{-42, -6, -7}, {11,29}, {-2}, {1, 10}} F. P = {{-42,-6}, {11, 29}, {−7, −2}, {1,10}}

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 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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Q6 I need correct and perfect soloution plz take ur time and solve perfectly plz and show neat and clean handwriting plz
QUESTION 6. Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For all x, y € A, xRy if and only if x = y (mod 9). Given that R is an equivalence relation on A, which one of the following sets P is a partition of A into equivalence classes of R? A. P = {{-42}, {-6}, {-7, 11}, {29,-2}, {1}, {10}} B. P ={{-42, -7, -6, -2, 1, 10, 11, 29}} C. P ={{-42, -7,-6}, {-2, 1}, {10, 11,29}} D. P ={{-42,-6}, {-7, 11,29}, {-2}, {1, 10}} E. P ={{-42, -6, -7}, {11, 29}, {-2}, {1, 10}} F. P ={{-42,-6}, {11, 29}, {-7, -2}, {1,10}}
Transcribed Image Text:QUESTION 6. Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For all x, y € A, xRy if and only if x = y (mod 9). Given that R is an equivalence relation on A, which one of the following sets P is a partition of A into equivalence classes of R? A. P = {{-42}, {-6}, {-7, 11}, {29,-2}, {1}, {10}} B. P ={{-42, -7, -6, -2, 1, 10, 11, 29}} C. P ={{-42, -7,-6}, {-2, 1}, {10, 11,29}} D. P ={{-42,-6}, {-7, 11,29}, {-2}, {1, 10}} E. P ={{-42, -6, -7}, {11, 29}, {-2}, {1, 10}} F. P ={{-42,-6}, {11, 29}, {-7, -2}, {1,10}}
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