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The binary operation * is defined by `a*b=(a b)/7` on the set `Q` of all rational numbers. Show that * is associative.

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* is defined by `a`*`b=(a b)/7` on the set `Q`
Then we have to prove that * is associative.
Now let `a,b,c in Q`
Then
`(a`*`b)`*`c=((ab)/7)`*`c`
`(a`*`b)`*`c=(((ab)/7)c)/7`
`(a`*`b)`*`c=(abc)/49 ldots (i)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. On Z , the set of all integers, a binary operation * is defined by ...

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

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

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

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

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

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

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

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

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

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  11. Find the identity element in the set I^+ of all positive integer...

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  12. Find the identity element in the set of all rational numbers except ...

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  13. If the binary operation * on the set Z is defined by a*b=a+b-5, then ...

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  14. On the set Z of integers, if the binary operation * is defined by a...

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

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  16. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

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  17. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

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  18. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  19. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  20. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for...

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