I am trying to solve the following task: If $x=1$ or $y=0$ then $z=0$
If $z=0$ then $x+y \le 2 + Mz \implies x+y \le 2+2z \quad$ where $M = 2$
If $z=1$ then $x+y=1 \\ \implies x+y \le 1, \quad x+y \ge 1 - M(1-z) \\ \implies x+y \ge z$
where $M = 1$
I already tried to add the constraint: $y-x \ge 0$ to ensure that combination $x=1, y=0, z=1$ should be satisfied and combination $x=1, y=0, z=1$ should be not satisfied.
But then the combination $x=1, y=0, z=0$ isn’t satisfied, although it should be.
In 1 combination the sum of $x+y = 2$.
I would be grateful for any hints regarding the task or showing where my approach is wrong.