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…

Math

Advanced Math

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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