Let $M =$ the set of odd numbers. Clearly if we delete one $m$ number from $M$ to form $N = M\setminus \{x\}$, then $\Delta N := N -N$ still equals $2\Bbb{Z}$.
Now let $N_X := M\setminus X$ for any $X \subset M$, where for singletons $X = \{x\}$ we just write $N_x$. Then:
$$
\Delta N_c \cap \De...