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Problem 4.4. Let D=Q\{0}, the set of all non-zero rational numbers. For all r, yED, define c*y = 4cy, the ordinary product of

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D O » xxy = 4xy Given X, Y ED To prove that (0*) is a group :) closure :- let X, Y EQo = D. . * a*y = 4x4 a clearly 4xYED. >a) Identily :- let &, et D. where o e in the dentity element in D. ņ ate =a = exa. ņ1 exx :x 4Xe = x from (C#) AssociativityInverse property, let a, y ED. exy se - 4xy = | y = ED and 4x2 = Ñ as .164 y = + ED left inverse = Right inverse inverse of s

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