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Q, the set of all rational number, * is defined by `a*b=(a-b)/2` , show that * is no associative.

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* is defined by `a`*`b=(a-b)/2` on the set `Q`
Then we have to prove that * is not associative.
Now let `a,b,c in Q`
Then
`(a`*`b)`*`c=((a-b)/2)`*`c`
`(a`*`b)`*`c=(((a-b)/2)-c)/2`
`(a`*`b)`*`c=(a-b-2c)/4 ldots (i)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  18. On Q, the set of all rational numbers, a binary operation * is defined...

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