I am completely stuck on the following problem. Let $P^i = \{x \mid A^i x \leq b^i \}$ for $i=1,2$. Derive a system of linear inequalities which is feasible if and only if $P^1 = P^2$.
It is easy to come up with a system of linear inequalities that is feasible if and only if $P^1$ and $P^2$ intersect, but I can't come up with a system that shows that $P^1 = P^2$.
