1. ## binary operation

The given set is R-{-1}

* is defined as a*b = a/[b+1]

The question is whether * is a binary operation.

My gut feeling was * should be a binary operation.

So I tried to prove by contradiction.

a is not equal to -1.

b is not equal to -1.

I assumed a*b = a/[b+1] = -1

a + b + 1 = 0

I got stuck.

What to do?

whether it is a binary operation or not?

Is there any other way to proceed?

kindly guide me.

with warm regards,

Aranga

2. ## Re: binary operation

Originally Posted by arangu1508
The given set is R-{-1}

$\circ$ is defined as a$\circ b = \dfrac{a}{b+1}$
The question is whether * is a binary operation.
My gut feeling was * should be a binary operation.
So I tried to prove by contradiction.
What is $\large {1\circ-2=~?}$

So does $\bf{\circ}$ mapp $R\setminus\{-1\}\times R\setminus\{-1\}\to R\setminus\{-1\}~?$ ans: No. why?

Now the answer really depends upon how binary operation is defined in your course

3. ## Re: binary operation

It is given as * on R-{-1}.

Thank you. I think it is not a binary operation.

with warm regards,

Aranga

4. ## Re: binary operation

You said
The given set is R-{-1}

* is defined as a*b = a/[b+1]

The question is whether * is a binary operation
My first reaction would be that a and b are two objects so, yes, this is a binary operation. If the question had been "is this a binary operation on R- {-1}", so that every (a, b) with both a and b in R- {-1} is mapped to a member of R-{-1}, then I would say no because of Plato's example.

5. ## Re: binary operation

Thanks. I understood the difference.

The question is what is defined as * on R-{-1} is to be tested whether it is a binary operation or otherwise.

with warm regards

Aranga