Please help me answer it? C. (3 points each) Determine whether the binary operation gives a group structure on a givenset by showing that this structure satisfies the group axioms. If no, identify the group axiomthat does not hold, and determine if it forms a semigroup or a monoid on a given set.(11) The pair (Z, *) in which a y = r +y +ry.(12) The pair (R+, *) in which r* y = VTy.(13) The pair (Q. *) in which r*y = (r+y)/3.(14) The pair (R × R, +) in which (w, z) * (y, z) = (wz + ry, rz).(15) The pair (Q-{-1}, +) in which ry = r + y + xy.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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