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(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.

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(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.

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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.