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If * defined on the set R of real number...

If * defined on the set R of real numbers by `a*b=(3a b)/7` , find the identity element in R for the binary operation *.

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Let `e in R` be identity element.
` therefore a * e=a forall a in R `
` Rightarrow frac{3 a e}{7}=a `
` Rightarrow e=frac{7 a}{3 a} `
` Rightarrow e=frac{7}{3}`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. Find the identity element in set Q^+ of all positive rational numbers ...

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

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

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

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  8. If the binary operation o. is defined on the set Q^+ of all positive r...

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  9. Let S={a+sqrt(2)\ b\ : a ,\ b in Z}dot Then, prove that an operati...

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  10. Let S={1,\ 2,\ 3,\ 4} and * be an operation on S defined by a*b=r , wh...

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  12. Show that the operation vv and ^^ on R defined as avvb= Maximum of ...

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  13. On the set Q of all rational numbers an operation * is defined by a*b ...

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  14. On the set W of all non-negative integers * is defined by a*b=a^b ....

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  15. On the set C of all complex numbers an operation 'o' is defined by ...

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  16. Let M be the set of all singular matrices of the form [xxxx] , wher...

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  17. Determine whether * on N defined by a*b=a^b for all a ,\ b in N de...

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  18. Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in ...

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  19. Determine whether * on N defined by a*b=a+b-2 for all a ,\ b in N ...

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