I have the following exercise: List all possible equivalence relations on the set (1,2,3,4) without repetition up to isomorphism. Justify your answer. (Q2)I tried to solve it and got the solution which is attached. However, I feel like something is not correct, maybe I understood the question wrong? The course is abstract algebra so help is much appreciated 9소STAHence, R3 is not transitive.✓Chс-D Since R3 is not symmetric and not transitive, R3 is not an equivalencerelationQ2:No. of partitions of a set: 2^-1 = 2ª - 1 =15.Hence: {{1,2,3,43}, {{1},{2,3,4}},{{2},{1,3,4}}, {{33. {1,2,413}, {{4}, {1,2,333},{ § 1,2}, {3,4} }, {§ 1.43,£2,33}, §§1,3}, {2,4}} §£1,2},{3}{433,§ §1.33. {2}, {4}}.§£1.45,{2},{3}},{$13, 52167 18433.{{1}, { 2,4}, {3}}, { {^}, {2}, {3,43}, {{1}, {2}, {3}, {4}}3:i) (R², $), where (x,y)* (a,b) = (x+a, y-b). (12²= {(2,W): Z, WER}a) let (x,y),(a,b) ETR², where x, y, a, b ER↳₂ (x+a). (y-b) → (x+a₁ y-b) € 12².19(ANSLATGEMEEP+: 02 معامل مد>219>+

Introduction: An equivalence relation is a binary relation on a set that satisfies three properties:…

Answered: List all possible equivalence relations…

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List all possible equivalence relations on the set (1,2,3,4) without repetition up to isomorphism. Justify your answer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 7RE

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Question

I have the following exercise:

List all possible equivalence relations on the set (1,2,3,4) without repetition up to isomorphism. Justify your answer. (Q2)

I tried to solve it and got the solution which is attached. However, I feel like something is not correct, maybe I understood the question wrong? The course is abstract algebra so help is much appreciated

9
소
S
TA
Hence, R3 is not transitive.
✓
Ch
с
-D Since R3 is not symmetric and not transitive, R3 is not an equivalence
relation
Q2:
No. of partitions of a set: 2^-1 = 2ª - 1 =15.
Hence: {{1,2,3,43}, {{1},{2,3,4}},{{2},{1,3,4}}, {{33. {1,2,413}, {{4}, {1,2,333},
{ § 1,2}, {3,4} }, {§ 1.43,£2,33}, §§1,3}, {2,4}} §£1,2},{3}{433,
§ §1.33. {2}, {4}}.§£1.45,{2},{3}},{$13, 52167 18433.
{{1}, { 2,4}, {3}}, { {^}, {2}, {3,43}, {{1}, {2}, {3}, {4}}
3:
i) (R², $), where (x,y)* (a,b) = (x+a, y-b). (12²= {(2,W): Z, WER}
a) let (x,y),(a,b) ETR², where x, y, a, b ER
↳₂ (x+a). (y-b) → (x+a₁ y-b) € 12².
1
9
(ANSLAT
GEMEE
P
+: 0
2 معامل مد
>
219
>
+

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