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A binary operation on a set S is a funct...

A binary operation on a set S is a function from

A

`S to S`

B

`(S xx S) to S`

C

`S to (S xx S)`

D

`(S xx S) to (S xx S)`

Text Solution

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The correct Answer is:
B
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Explore conceptually related problems

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

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

  • A binary operation on a set Sis a function from

    A
    `S xxS`
    B
    `(SxxS)toS`
    C
    `S to (Sxx S)`
    D
    `(S xxS)to(SxxS)`

  • - is a binary operation on

    A
    ~
    B
    Q-{0}
    C
    R-{0}
    D
    Z

  • The binary operation ** defined on a set s is said to be commutative if

    A
    `a**b in S AA a, b in S`
    B
    `a ** b =b ** a AA a, b in S`
    C
    `(a ** b) ** c =a ** (b ** c) AA a, b in S`
    D
    `a ** b = e AA a, b in S`

    • Similar Questions

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    Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary opertion on R. Further, show that division is binary opertion on the set R, of nonzero real numbers.

    State whether the following statements are true or false, Justify. (i) For an arbitraty binary opertion ** on a set N, a**a =a AA a in N. (ii) If ** is a commutative binary opertion on N, then a ** (b **c) = (c**b) *8a

    Determine whether ** is a binary operation on the sets given below. a**b=a.|b| on RR

    Determine whether ** is a binary operation on the sets given below. (a**b)=a sqrt(b) is binary on RR

    + is not a binary operation on

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