Let $G = \mathbb{Q}\setminus\{1\}$ be the set of all rational numbers other than $1$ and suppose $*$ is defined as $a*b=a+b-ab$. Show that $*$ is a binary operation on $G$.
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Possible duplicate of Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} - {-1}$, resp. http://math.stackexchange.com/questions/2184693/prove-that-a-b-a-b-ab-defines-a-group-operation-on-bbb-r-setminus – Dietrich Burde Apr 02 '17 at 18:54
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The following is true even when replacing $\mathbb R$ with $ \mathbb Q$ – amWhy Apr 02 '17 at 19:03
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We only need to show it defines a function from $G\times G\to G$. This follows since $a+b-ab=1$ and $b\neq 1$ \implies $a=(1-b)/(1-b)=1$.
Did you mean group (as opposed to binary) operation?
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