Binary operation defined as $a*b=a+b-ab$

Asked May 27 '17 at 05:14

Active May 27 '17 at 10:32

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Binary operation '*' defined as $a*b=a+b-ab$ on a set $A=R\setminus\left\{0,1\right\}$ where $R$ is Set of Reals

Is this binary operation closed under the above operation on above set $A$

I thought it is not closed since if $a=b=2$ then $$2*2=0$$ which is not in set $A$.

But my book answer is It is closed. What is my error?

edited May 27 '17 at 10:32

Michael Rozenberg

asked May 27 '17 at 05:14

Umesh shankar

2

You have made no error. The book is wrong. – Parcly Taxel May 27 '17 at 05:17
If the set is as you have defined it and the binary operation is as you've defined it then the set is not closed under that operation. – Tucker May 27 '17 at 05:18
It should say $A=\Bbb R-{1}$. Then $A$ is a group isomorphic to $\Bbb R^\times$. Good catch. – anon May 27 '17 at 05:32
My book says since $0,1$ are not in the Set, the pair $(2,2)$ will not be in the domain of Binary operation as Binary operation is a function from $A\times A$ to $A$. So the binary operation is closed. – Umesh shankar May 27 '17 at 17:35
any comment please? – Umesh shankar May 29 '17 at 03:18

0 Answers0