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Check the commutativity and associati...

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

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* is defined by `a`*`b=a-b` on the set `Z`
Then we have to prove that * is associative.
Now let `a,b,c in Z`
Then
`(a`*`b)`*`c=(a-b)`*`c`
`(a`*`b)`*`c=a-b-c ldots (i)`
`a`*(`b`*`c`)`=a`*`(b-c)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  9. On the set Z of integers a binary operation * is defined by a*b=a b...

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  10. Let S be the set of all real numbers except -1 and let * be an oper...

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  15. On Q , the set of all rational numbers a binary operation * is defi...

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  16. Let S be the set of all rational number except 1 and * be defined ...

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  17. Let S be the set of all rational number except 1 and * be defined ...

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  18. If * defined on the set R of real numbers by a*b=(3a b)/7 , find the i...

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  19. Find the identity element in set Q^+ of all positive rational numbers ...

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  20. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

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