Let \( Q_{0} \) be the set of all nonzero rational numbers. Let \( ...

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Let \( Q_{0} \) be the set of all nonzero rational numbers. Let \( * \) be a binary
\( \mathrm{P} \) operation on \( Q_{0} \), defined by \( a * b=\frac{a b}{4} \) for all \( a, b \in Q_{0} \).

W \( * \) is associative.
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