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Let S be the set of all rational num...

Let `S` be the set of all rational number except 1 and * be defined on `S` by `a*b=a+b-a b ,` for all `a ,bSdot` Prove that (i) * is a binary operation on `( i i ) * is commutative as well as associative.

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. On Q , the set of all rational numbers a binary operation * is defin...

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  2. Let S be the set of all rational number except 1 and * be defined ...

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  3. Let S be the set of all rational number except 1 and * be defined ...

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

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

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

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

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  9. Find the identity element in the set I^+ of all positive integers ...

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  10. Find the identity element in the set of all rational numbers except ...

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

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  12. On the set Z of integers, if the binary operation * is defined by a*...

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  13. On Q, the set of all rational numbers, a binary operation * is defined...

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  14. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

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  15. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

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

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

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  18. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for ...

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  19. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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  20. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

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