The following is the question from my Introduction to Discrete math book:

The addition and multiplicationof real numbers are functions add, multi: R x R --> R, where:

add(x, y) = x + y; multi(x, y) = xy

a.) Is add ont-to-one? Is it onto?

b.) Is Multi one-to-one? Is it onto?

I know the answer to a.) because the book gives the answer but have confused myself on how it is obtained. Is it possible to get an explanation of the following answer for a.)

a. answer)Add is not one-to-one, since add (1, 1) = add (0, 2), while (1, 1) (0, 2).It is onto, because for any y R, the equation y= add(x) has the solution x= (y, 0)

I am either not remembering something simple or have missed something. Please help explain how the answer to a.) is obtained. Thanks!