For each binary operation * defined on a set below, determine whether or not * gives a group structure on the set. If it is a group, explain why it is a group. If it is not a group, say which axioms fail to hold: (a) Define * on Z by a * b max(a, b). %3D (b) Define * on Q \ {0} by a * b = |ab|. (c) Define * on Q+ by a * b = ab.

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