Properties of subgroups


Question:

Properties of subgroups

Let A be a group and let Z be a subgroup of A. Let x,y be elements of G. Tell if each statement is true of false and give reason

1) if Zx = Zy then xZ = yZ
2) if Zx = Zy then Zxy-1 = Z
3) if Zx = Zy then Zx2=Zy2

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Algebra: Properties of subgroups
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