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Check the commutativity and associati...

Check the commutativity and associativity of * on `Q` defined by `a*b=(a b)/4` for all `a ,\ b in Q` .

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* is defined by `a`*`b=(a b)/4` on the set `Q`
Then we have to prove that * is associative.
Now let `a,b,c in Q`
Then
`(a`*`b)`*`c=((ab)/4)`*`c`
`(a`*`b)`*`c=(((ab)/4)c)/5`
`(a`*`b)`*`c=(abc)/16 ldots (i)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  9. Let S be the set of all real numbers except -1 and let * be an oper...

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  10. Q, the set of all rational number, * is defined by a*b=(a-b)/2 , show ...

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  12. On the set Q of all rational numbers if a binary operation * is def...

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  13. The binary operation * is defined by a*b=(a b)/7 on the set Q of al...

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

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

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

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

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

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

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  20. Let S be a non-empty set and P(s) be the power set of set S. Find the ...

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