In a BIP problem with $2$ mutually exclusive alternatives, $x_1$ and $x_2,$ the following constraint needs to be added to the formulation if one alternative must be chosen:

None of the choices is correct.

$x_1+x_2=1$

$x_1+x_{2}1$

$x_1-x_{2}1$

$x_1-x_2=1$