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Show that the number of binary operation...

Show that the number of binary operations on `{1," "2}` having 1 as identity and having 2 as the inverse of 2 is exactly one.

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Given that `1` is identity then `a*1=1*a=a`.
`a=1`
`1*1=1`
`a=2`
`1*2=2*1=1`
Given that `2` is inverse of `2`
`e=2` and `a=2, b=2`
`2*2=2*2=1` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Con...

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  19. Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on...

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  20. \begin{tabular}{|l|l|l|l|l|l|} \hline 1 & 1 & 2 & 3 & 4 & 5 \\ \hline ...

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