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Let * be a binary operation o Q defined ...

Let * be a binary operation o Q defined by a*b= `(ab)/4` for all a,b`in` Q ,find identity element in Q

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`a**e=e**a=a `
` a** e=frac{a e}{4}= a `
` e=4`
`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

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

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  3. Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,bin Q...

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

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

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

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  7. Let S=(0,1,2,3,4,) and * be an operation on S defined by a*b=r , where...

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

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

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

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

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

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

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

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

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  16. Determine whether 'xx6' on S={1,\ 2,\ 3,\ 4,\ 5} defined by axx6b= Rem...

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  17. Determine whether '+6' on S={0,\ 1,\ 2,\ 3,\ 4,\ 5} defined by a+6b={a...

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  18. 'o' on N defined by a o b= a b + b a for all a, b∈N define...

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  19. '*' on Q defined by a*b=(a-1)/(b+1) for all a ,\ b in Q define a bina...

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  20. Determine whether or not the definition of * On Z^+ , defined * by ...

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