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