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

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

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter1: Line And Angle Relationships
Section1.6: Relationships: Perpendicular Lines
Problem 18E: Does the relation is in love with have a reflexive property consider one person? a symmetric...
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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 > +
Transcribed Image Text: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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