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Write the identity element for the binary operations * on the set `R_0` of all non-zero real numbers by the rule `a*b=(a b)/2` for all `a ,\ b in R_0`

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The given binary operation is `a^{*} b=a b / 2`
And from the definition of identity element e,
`a^{*} e=a ldots ldots . .(i)`
We have,
`a^{*} e=a e / 2`
Thus from (i) & (ii), ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Consider the binary operation * and o defined by the following t...

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  2. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

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  3. Write the identity element for the binary operations * on the set R...

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  4. On the set Z of all integers a binary operation * is defined by a*b...

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  5. Define a binary operation on a set.

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  6. Define a commutative binary operation on a set.

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  7. Define an associative binary operation on a set.

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  8. Write the total number of binary operations on a set consisting of ...

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  9. Write the identity element for the binary operation * defined on th...

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  10. Let * be a binary operation, on the set of all non-zero real number...

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  11. Write the inverse of 5 under multiplication modulo 11 on the set {1...

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  12. Define identity element for a binary operation defined on a set.

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  13. Write the composition table for the binary operation multiplication...

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  14. Write the composition table for the binary operation multiplication ...

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  15. For the binary operation multiplication modulo 5\ (xx5) defined on ...

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  16. Write the composition table for the binary operation xx5 (multiplic...

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  17. A binary operation * is defined on the set R of all real numbers by...

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  18. Let +6 (addition modulo 6) be a binary operation on S={0,\ 1,\ 2,\ ...

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  19. Let * be a binary operation defined by a*b=3a+4b-2 . Find 4*5.

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  20. If the binary operation * on the set Z of integers is defined by...

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