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Find the identity element in set `Q^+` of all positive rational numbers for the operation * defined by `a*b=(a b)/2` for all `a , b in Q^+dot`

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Find the identity element in the set of all rational numbers except -1 with respect to * defined by a*b= a+b+a b .

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let S be the set of all rational numbers except 1 and * be defined on ...

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  2. Q, the set of all rational number, * is defined by a * b=(a-b)/2 , sho...

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  3. Find the identity element in set Q^+ of all positive rational numbers ...

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

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  5. Let S be a non-empty set and P(s) be the power set of set S. Find the ...

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

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

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

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

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

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

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

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

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

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

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

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  17. Let M be the set of all 2X2 real singular matrices . On M , let * be...

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

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

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

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