Let * be a binary operation defined on Q. Det | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) binary operation $*$ on a set $S$ is commutative if $a * b = b * a$ for all $a, b \in S$. Given the operation $a * b = a - b$ for all $a, b \in Q$

Vedclass · Accepted Answer

No,it is not commutative.

Vedclass · Answer

(B) binary operation $*$ on a set $S$ is commutative if $a * b = b * a$ for all $a, b \in S$. Given the operation $a * b = a - b$ for all $a, b \in Q$. To check for commutativity,we calculate $b * a$: $b * a = b - a$. Now,compare $a * b$ and $b * a$: $a * b = a - b$ and $b * a = b - a$. Since $a - b 
eq b - a$ in general (for example,let $a = 5$ and $b = 3$,then $5 - 3 = 2$ while $3 - 5 = -2$,and $2 
eq -2$),the operation is not commutative. Therefore,the binary operation $*$ is not commutative.

Let $$ be a binary operation defined on $Q$. Determine whether the binary operation defined by $a b = a - b$ for all $a, b \in Q$ is commutative.

Similar Questions

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a ^ b = a - b$. Determine whether the operation $^*$ is commutative and associative.

On the set of positive rationals,a binary operation $$ is defined by $a b = \frac{2ab}{5}$. If $2 * x = 3^{-1}$,then $x = $

On the set $Z$ of all integers,the operation $$ is defined by $a b = a + b - 5$. If $2 * (x * 3) = 5$,then $x$ is equal to:

Let $^$ be the binary operation on $N$ given by $a \, ^ \, b = \text{L.C.M. of } a \text{ and } b$. Is $^*$ commutative?

Which of the following is not a group with respect to the given operation?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $*$ be a binary operation defined on $Q$. Determine whether the binary operation defined by $a * b = a - b$ for all $a, b \in Q$ is commutative.