If is a binary operation on a set S why is it not possible t

If is a binary operation on a set S, why is it not possible that st could have two possible answers in S?

Solution

A binary operation on a set S is a mapping that assigns to each ordered pair of elements of S a uniquely determined element of S. Thus, by definition itself, st is a uniquely determined element of S and therefore, it cannot have two possible answers in S.