# conditional constraints -Integer programming

I am trying to solve the following question: Consider the constraints $a_i \le f_i(x) \le b_i$ $i=1,2,3$ and $a_i$ and $b_i$ are given constants for all $i$. Show the following conditional constraints can be expressed as a manageable forms by using 0-1 varibles:

i) $f_1(x) \ge 0$ then $f_2(x) \ge 0$

ii) $f_1(x) \ge 0$ then $f_2(x) \ge 0$ and $f_1(x) \le 0$ then $f_3(x) \ge 0$

I am ok with i) but for ii) I started by doing the equivalent tersm thatare $f_1 \le 0$ or $-f_2 \le 0$ and $-f_1 \le 0$ or $-f_3 \le0$. But I am not sure if I have to select $M_1$ and $M_2$ such that $M_1 \ge max f_1, -f_2$ and $M_2 \ge max -f_1 , -f_3$ then let $y_i$ is a binary variable such that

$f_1 \le M_1y_1$ , $-f_2 \le M_1(1-y_1)$

$-f_1 \le M_2y_2$ , $-f_3 \le M_2(1-y_2)$

Can anyone tell where is the mistake if any?