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 $a b = a$

Open in App

Solution

On $Z^{+}$ , defined $$ by $a b = a$
It is seen that for each $a, b \in Z^{+}$ , there is a unique element $a \in Z^{+} .$
This means that $$ carries each pair (a,b) to a unique element $a b$ =a in $Z^{+} .$
Therefore, $*$ is a 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.
(iv) On $Z^{+}$ , defined $a * b = | a - b |$

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 $a * b = a b^{2}$

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 $Z^{+}$ , defined $*$ by $a * b = a - b$

(ii) On $Z^{+}$ , defined $*$ by $a * b = a b$

(iii) On R, defined $*$ by $a * b = a b^{2}$

(iv) On $Z^{+}$ , defined $a * b = | a - b |$

(v) On $Z^{+}$ , defined $*$ 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, 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

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. (v) On Z+, defined ∗ by a∗b=a

On Z+, defined ∗ by a∗b=a It is seen that for each a,b∈Z+, there is a unique element a∈Z+. This means that ∗ carries each pair (a,b) to a unique element a∗b =a in Z+. Therefore, ∗ is a 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.
(v) On $Z^{+}$ , defined $$ by $a b = a$

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