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Let * be a binary operation on Q defind ...

Let * be a binary operation on Q defind by `a*b= (ab)/(2), AA a,b in Q` Determine whether * is associative or not.

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The correct Answer is:
* is associative
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Let * be a binary operation on Q, defined by a * b =(ab)/(2), AA a,b in Q . Determine whether * is commutative or associative.

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Knowledge Check

  • Binary operation * on R - {-1} defined by a * b= (a)/(b+a)

    A
    * is associative and commutative
    B
    * is neither associative nor commutative
    C
    * is commutative but not associative
    D
    * is associative but not commutative

  • Binary operation * on R -{-1} defined by a ** b = (a)/(b+1) is

    A
    * is associative and commutative
    B
    * is associative but not commutative
    C
    * is neither associative nor commutative
    D
    * is commutative but not associative

  • Let ** be a binary defined on R by a**b=(a+b)/(4)AAa,binR then the operation ** is

    A
    a.Commutative and Associative
    B
    b.Commutative but not Associative
    C
    c.Associative but not commutative
    D
    d.Neither Associative nor Commutative

    • Similar Questions

    Explore conceptually related problems

    Let * be a binary operation on the set R defined by a ** b = (a + b)/2 . Show that * is commulative but not associative.

    Let * be the binary operation on N given by a * b =LCM of a and b, a AA a, b N. Find 5 * 7.

    Let * be a binary operation on N defined by a ** b = HCF of a and b. Show that * is both commutative and associative.

    Let ** be the binary opertion on N defined by a **b=H.C.F. of a and b. Is ** commutative ? Is ** associative ? Does there exist identity for this binary opertion on N ?

    Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find 5 * 7.

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