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Let * be a binary operation on Q, define...

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

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

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

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

    A binary operation * on N defined as a ** b = sqrt(a^(2) + b^(2)) , show that * is both cummutative and associative.

    Let * be a Binary operation on the set Q of rational number's by a * b = (a -b)^(2) . Prove that * is commutative.

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    A binary operation * on N defined as a ** b = a^(3) + b^(3) , show that * is commutative but not associative.

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