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On the set Q of all rational numbers ...

On the set `Q` of all rational numbers if a binary operation * is defined by `a*b=(a b)/5` , prove that * is associative on `Qdot`

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* is defined by `a`*`b=(a b)/5` on the set `Q`
Then we have to prove that * is associative.
Now let `a,b,c in Q`
Then
`(a`*`b)`*`c=((ab)/5)`*`c`
`(a`*`b)`*`c=(((ab)/5)c)/5`
`(a`*`b)`*`c=(abc)/25 ldots (i)`
...
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