Determine whether or not each of the definition of ' \( * \) ' given below gives a binary operat...

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Determine whether or not each of the definition of ' \( * \) ' given below gives a binary operation. In the event that ' \( * \) ' is not a binary operation, give justification.
On \( \mathrm{Z}^{+} \), defined by \( a * b=a-b \) where \( \mathrm{Z}^{+} \)is the set of non-negative integers.
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