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Let A=Nuu{0}xxNuu{0} and let * be a bina...

Let `A=Nuu{0}xxNuu{0}` and let * be a binary operation on `A` defined by `(a ,\ b)*(c ,\ d)=(a+c ,\ b+d)` for all `(a ,\ b),\ (c ,\ d) in Adot` Show that * is associative on `Adot`

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Let `(a,b),(c,d)` and `(e,f)` belongs to `A`
`{(a,b)∗(c,d)}∗(e,f)=(a+c,b+d)∗(e,f) =(a+c+e,b+d+f)....(4)` ​
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)...

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  2. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

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  3. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

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  4. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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  5. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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  6. Show that the number of binary operations on {1," "2} having 1 as iden...

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  7. Determine the total number of binary operations on the set S={1,\ 2...

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  8. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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  9. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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

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  11. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for all...

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  12. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for al...

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  13. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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  14. Let 'o' be a binary operation on the set Q0 of all non-zero rati...

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  15. On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that...

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  16. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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  17. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

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  18. Let * be the binary operation on N defined by a*b=H C F of a and b ...

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  19. Consider the set S={1,\ -1} of square roots of unity and multiplica...

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  20. Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity...

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