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    Defining a group using axioms.

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    Define * on Z by a * b = max{a,b}. Is Z a group?

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    No, Z is not a group under this definition.
    We can not find the identity of the group.
    If 0 is the identity, then (-1)*0=(-1). But by the definition, ...

    Solution Summary

    Group status is determined using axioms. The details are well presented in the solution.