Prove that each of the following sets, with the indicated operation, is an abelian group.(a) (R, *) with the operation x*y=x+y+c for each x, y € R, where c E R is a constant.(b) (R*, *) with the operation x * y = for each x, y E R*.xy2(c) (R \ {-1}, *) with the operation x * y = x + y + xy for each x, y ≤ R \ {-1}.

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Answered: Prove that each of the following sets,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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