please send handwritten solution Q8 8. Let A = Z* U {0}, define relation R on A × Z* by (k, l)R(m,n) → kn = lm.(a). Prove that Ris an equivalence relation.(b). What are the elements of A x Z* in the equivalence class [(1,2)]?

In part (a) we use the definition of equivalence relation i.e., reflexive, symmetric and transitive.…

Answered: 8. Let A = Z* U {0}, define relation R…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...

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8. Let A = Z* U {0}, define relation R on A × Z* by (k, l)R(m,n) → kn = lm. (a). Prove that Ris an equivalence relation. (b). What are the elements of A x Z* in the equivalence class [(1,2)]?