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For each operation ** defined below, det...

For each operation `**` defined below, determine , whether `**` is binary , commutative or associative.
On `Z^(+)` , define `a "*" b =ab`

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The correct Answer is:
`:. **` is not associative on `Z^+`
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Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = |a-b|

Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On Z^(+) , define ** by a" * " b = a

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Determine whether or not each of the definition of ** given below gives a binary operation. In the even that ** is not a binary operation , give justification for this . On R , define ** by a" * " b = ab^2

A binary operation ** be defined on the set R by a**b = a+b +ab . Show that ** is commutative, and it is also Associative.

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -EXERCISE 1.3
  1. Consider f : R rarr R given by f(x) = 4x +3. Show that f is invertibl...

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  2. Consider f: R ^+ to [4 ,oo] given by f(x) =x^2 + 4 show th...

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  3. Consider f : R(+) rarr [-5,oo) given by f(x) = 9x^(2) +6x-5. Show that...

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  4. Let f :X rarr Y be an invertible function . Show that f has unique inv...

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  5. Consider f : {1,2,3} rarr {a,b,c} given by f(1) = a, f(2) and f(3) = ...

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  6. Let f : X rarr Y be an invertible function . Show that the inverse of ...

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  7. If f : R rarr R be given by f(x) = (3-x^(3))^(1/3) then fof (x) is

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  8. Let f: R -{-4/3}rarrR be a function defined as f(x) =(4x)/(3x+4) . Th...

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  9. Determine whether or not each of the definition of ** given below give...

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  10. Determine whether or not each of the definition of ** given below give...

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  11. Determine whether or not each of the definition of ** given below give...

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  12. Determine whether or not each of the definition of ** given below give...

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  13. Determine whether or not each of the definition of ** given below give...

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  14. For each opertion ** difined below, determine whether ** isw binary, c...

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  15. For each opertion ** difined below, determine whether ** isw binary, c...

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  16. For each opertion ** difined below, determine whether ** isw binary, c...

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  17. For each opertion ** difined below, determine whether ** isw binary, c...

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  18. For each operation ** defined below, determine , whether ** is binar...

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  19. For each opertion ** difined below, determine whether ** isw binary, c...

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  20. Consider the binary operation ^^ on the set {1,2,3,4,5} defined by a^^...

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