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If the operation * is defined on the set `Q` of all rational numbers by the rule `a`*`b=(a b)/3` for all `a ,\ b in Q` . Show that * is associative on `Q`

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Let * be a binary operation on `Q`
And it is defined by `a`*`b=(a b)/3`
Then we have to prove that * is associative on `Q`
As , `a`*`b=(ab)/3`
Let a,b,c Q
`(a`*`b)`*`c=((ba)/2)`*`c`
`(a`*`b)`*`c=(abc)/9`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. Let A be a set having more than one element. Let * be a binary opera...

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  3. If the operation * is defined on the set Q of all rational numbers ...

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  4. Examine whether the binary operation ** defined on R by a**b=a b+1 i...

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  5. Let A be a set having more than one element. Let * be a binary opera...

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  6. Discuss the commutativity and associativity of the binary operation * ...

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  7. Discuss the commutativity and associativity of the binary operation * ...

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  8. Discuss the commutativity and associativity of binary operation * d...

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  9. Let * be a binary operation on N, the set of natural numbers, defined ...

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  10. Let * be a binary operation on N given by a*b=H F C(a ,\ b) for all ...

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  11. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

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  12. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

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  13. Let A be a non-empty set and S be the set of all functions from A t...

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  14. Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*...

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  15. Let A be a set having more than one element. Let * be a binary oper...

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  16. Let * be a binary operation on N defined by a*b=1. cdotmdot(a ,\ b)...

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  17. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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  18. Determine whether * on N defined by a*b=1 for all a ,\ b in N is asso...

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  19. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

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  20. Let A be any set containing more than one element. Let * be a binar...

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