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Check the commutativity and associati...

Check the commutativity and associativity of * on `R` defined by `a*b=a+b-7` for all `a ,\ b in Q` .

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* is defined by `a`*`b=a+b-7` on the set `Q`
Then we have to check that * is associative and commutative or not .
Now let `a,b,c in Q`
Then
`(a`*`b)`*`c=(a+b-7)`*`c`
`(a`*`b)`*`c= a+b-7+c-7`
`(a`*`b)`*`c= a+b+c-14 ldots (i)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  20. Let S be the set of all rational number except 1 and * be defined ...

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