Chapter 8.1, Problem 63E

To determine

Whether the statement “f is a function of x and y if and only if for any two points $P_1\left(x_1,y_1\right)$ and $P_2\left(x_2,y_2\right)$ in the domain of f, $f\left(x_1,y_1\right)=f\left(x_2,y_2\right)$ implies that $P_1\left(x_1,y_1\right)=P_2\left(x_2,y_2\right)$” is true or false; if true explain the reason; if it is false explain with an example.