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6. (15 pts) Let G be a group. (a) (10 pts) Let 0 (b) (5 pts) Let 0 A,BCG and c E G. Suppose

 

6. (15 pts) Let G be a group. (a) (10 pts) Let 0 (b) (5 pts) Let 0 A,BCG and c E G. Suppose that cA= B. Prove that A=cB. X,Y CG and g E G. Use part (a) to prove that gXY if and only if X=gY. In each direction, clearly mention what A, B and care..

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