
EDIT: In steps (5), (6), (7) and (8) I replaced $n$ with $2n+1$ and in step (4) I changed $R$ to $L$
My initial answer to the question was incorrect but I think I have the right idea.
Consider the following group of sets
$T_1=\left\{\left.\frac{M_1(c_1)}{R_1(q_1)}\right|c_1,q_1\in\mathbb{Z}\r...