Question

Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b \[-\] ab, for all a, b \[\in\] S:

Prove that * is a binary operation on S ?

Answer 1

We have,

S = R \[-\] {1} and * is defined on S as a * b = a + b \[-\]ab, for all a, b \[\in\] S

It is seen that for each a, b \[\in\] S, there is a unique element a + b \[-\] ab in S

This means that * carries each pair (a, b) to a unique element a * b = a + b \[-\] ab in S

So, * is a binary operation on S