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A binary operaiton `@` is defined on the set `RR-{-1}` as `x@y=x+y+xy` for all `x,yinRR-{-1}.` Discuss the commutativity and associativity of `@` on `RR-{-1}.` If `(3**2x)**5=71,`, find x.

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The correct Answer is:
Commutative and associative, x=1
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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. An operation ** on ZZ, the set of integers, is defined as, a**b=a-b+ab...

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  2. (I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. ...

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  3. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  4. If ** be the binary operation on the set ZZ of all integers, defined b...

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  5. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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  6. Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,bi...

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  7. If +(6) (addition modulo 6) is a binary operation on A={0,1,2,3,4,5},...

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  8. A binary operation ** is defined on the set RR(0) for all non- zero re...

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  9. A binary operation ** is defined on the set ZZ of all integers by a@b=...

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  10. A binary operation ** is defined on the set of real numbers RR by a**b...

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  11. For the binary operation multiplication modulo 5*(xx(5)) defined on th...

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  12. A binary operation ** on QQ the set of all rational numbers is defined...

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  13. Prove that the identity element of the binary opeartion ** on RR defin...

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  14. Find the identity element of the binary operation ** on ZZ defined by ...

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  15. The binary operation * define on N by a*b = a+b+ab for all a,binN is

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  16. Prove that 0 is the identity element of the binary operation ** on ZZ^...

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  17. A binary operation ** on QQ(0), the set of all non-zero rational numbe...

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  18. A binary operation @ on QQ-{1} is defined by a**b=a+b-ab for all a,bin...

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  19. A binary operation ** on QQ, the set of rational numbers, is defined b...

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  20. Determine which of the following binary operations are associative and...

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