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Let ** be a binary operation on set Q of...

Let `**` be a binary operation on set Q of rational numbers defined as `a ** b= (ab)/8`. Write the identity for `**`, If any.

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(a) Write any three rational numbers

Let ** be a binary opertion on the set Q of rational numbers as follows: (i) a ***b =a -b (ii) a ** b =a^(2) + b ^(2) (iii) a **b =a + ab (iv) a ** b = (a-b) ^(2) (v) a **b = (ab)/(4) (vi) a **b =ab ^(2) Find which of the binary opertions are commutative and which are associative.

Knowledge Check

  • Number of binary opertions on the set {a,b} are

    A
    10
    B
    16
    C
    20
    D
    8

  • The operation ** defined by a ** b =(ab)/7 is not a binary operation on

    A
    `Q^(+)`
    B
    Z
    C
    R
    D
    C

  • A binary operation ** is defined on the set of positive rational number Q^(+) by a ** b =(ab)/4 . Then 3 ** (1/5 ** 1/2) is

    A
    `3/160`
    B
    `5/160`
    C
    `3/10`
    D
    `3/40`

    • Similar Questions

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    Find any seven rational numbers between 5/8 and -5/6

    In the set of integers under the operation * defined by a * b =a+b-5 then identity is:

    The number of binary operations that can be defined on a set of 3 elements is

    The operation ** defined by a**b=(ab)/(7) is not a binary operation on

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