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On the set Z of integers a binary ope...

On the set `Z` of integers a binary operation * is defined by `a*b=a b+1` for all `a ,\ b in Z` . Prove that * is not associative on `Zdot`

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

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  2. Show that the binary operation * on Z defined by a*b=3a+7b is not c...

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  3. On the set Z of integers a binary operation * is defined by a*b=a b...

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

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

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  6. On Z , the set of all integers, a binary operation * is defined by ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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