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State whether the following statements a...

State whether the following statements are true or false with reasons.
(i) For any binary operation `**` on `NN`, `a**a=aAAainNN`.
(ii) If `**`, a binary operation `**` on `NN` is commutative then, `a**(b**c)=(c**b)**a`.

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The correct Answer is:
(i) False (ii) True
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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Let S be any set containing more than two elements. A binary operation...

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  20. State whether the following statements are true or false with reasons...

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