You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Set Operation

Determine whe...

Question

Determine whether or not each of the definition of $$ given below gives a binary operation. In the event that $$ is not a binary operation, give justification for this.
(iii) On R, defined $$ by $a b = a b^{2}$

Open in App

Solution

On R, defined $$ by $a b = a b^{2}$
It is seen that for each $a, b \in R$ , there is a unique element $a b^{2}$ in R.
This means that $$ carries each pair (a,b) to a unique element $a b = a b^{2}$ in R. Therefore, $*$ is binary operation.

Suggest Corrections

Similar questions

Determine whether or not each of the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation, give justification for this.
(v) On $Z^{+}$ , defined $*$ by $a * b = a$

Determine whether or not each of the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation, give justification for this.
(iv) On $Z^{+}$ , defined $a * b = | a - b |$

Q. Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z + , define * by a * b = a − b (ii) On Z + , define * by a * b = ab (iii) On R , define * by a * b = ab 2 (iv) On Z + , define * by a * b = | a − b | (v) On Z + , define * by a * b = a

Q. Determine whether or not each of the definition of

*

given below gives a binary operation. In the event that

*

is not a binary operation, given justification for this
(i) On

Z^{+}

, define

*

a * b = a - b

(ii) On

Z^{+}

, define

*

a * b = a b

(iii) On

R

, define

*

a * b = a b^{2}

(iv) On

Z^{+}

, define

*

a * b = | a - b |

Z^{+}

, define

*

a * b = a

Determine wherther or not each of the defintion of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation, give justification for this.
(ii) ON $Z^{+}$ , defined $*$ by $a * b = a b$

Join BYJU'S Learning Program

Determine whether or not each of the definition of ∗ given below gives a binary operation. In the event that ∗ is not a binary operation, give justification for this. (iii) On R, defined ∗ by a∗b=ab2

On R, defined ∗ by a∗b=ab2 It is seen that for each a,b∈R, there is a unique element ab2 in R. This means that ∗ carries each pair (a,b) to a unique element a∗b=ab2 in R. Therefore, ∗ is binary operation.

Determine whether or not each of the definition of $$ given below gives a binary operation. In the event that $$ is not a binary operation, give justification for this.
(iii) On R, defined $$ by $a b = a b^{2}$

On R, defined $$ by $a b = a b^{2}$
It is seen that for each $a, b \in R$ , there is a unique element $a b^{2}$ in R.
This means that $$ carries each pair (a,b) to a unique element $a b = a b^{2}$ in R. Therefore, $*$ is binary operation.