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Consider a binary operation ** on N defi...

Consider a binary operation `**` on N defined as `a"*"b=a^(3)+b^3`. Choose the correct answer.

A

Is `**` both associative and commutative ?

B

Is `**` commutative but not associative ?

C

Is `**` associative but not commutative ?

D

Is `**` neither commutative nor associative ?

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The correct Answer is:
B
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -EXERCISE 1.4
  1. Let ** be the binary operation on N given by a**b = L.C.M. of a and b...

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  2. Let ** be the binary operation on N given by a**b = L.C.M. of a and b...

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  3. Is ** defined on the set {1,2,3,4,5} by a"*"b = L.C.M. of a and b a bi...

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  4. Let ** be the binary operation on N defined by a"*"b = H.C.F of a and ...

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  5. Let ** be a binary operation on the set Q of rational numbers as follo...

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  6. Let ** be a binary operation on the set Q of rational numbers as follo...

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  7. Let ** be a binary operation on the set Q of rational numbers as follo...

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  8. Let ** be a binary operation on the set Q of rational numbers as follo...

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  9. Let ** be a binary operation on the set Q of rational numbers as follo...

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  10. Let ** be a binary operation on the set Q of rational numbers as follo...

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  11. Find which of the operations given above has identity. a"*"b=a-b

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  12. Find which of the operations given above has identity. a"*"b=a^(2)+b...

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  13. For which values of p does the pair of equations given below has uniqu...

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  14. Find which of the operations given above has identity. a"*"b=(a-b)^2

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  15. Find which of the operations given above has identity. a"*"b=(ab)/4

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  16. Find which of the operations given above has identity. a"*"b=ab^2

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  17. L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c...

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  18. State whether the following statements are true or false . Justify . ...

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  19. State whether the following statements are true or false . Justify . ...

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  20. Consider a binary operation ** on N defined as a"*"b=a^(3)+b^3. Choose...

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