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In Exercises 15–20, let the binary operation p be defined on Z by the given rule. Determine in each case whether Z is a group with respect to p and whether it is an abelian group. State which, if any, conditions fail to hold. 15. x * y = x + y +1

- November 14, 2022 - Edwin Tunner

In Exercises 15–20, let the binary operation p be defined on Z by the given rule. Determine in each case whether Z is a group with respect to p and whether it is an abelian group. State which, if any, conditions fail to hold.
15. x * y = x + y +1

16. x * y = x + y – 1
17. x * y = x + xy

18. x * y = xy + y
19. x * y = x + xy + y

20. x * y = x – y

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