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Comparing Closure Among Various Operations

ABSALG-7COFYF

Let $A$, $S$, $M$, and $D$ denote the set of nonempty subsets of $\mathbb{Z}$ which are closed under addition, subtraction, multiplication, and division, respectively.

Identify all comparable relationships between these sets.

A

$A\subseteq S$ and $D\subseteq M$

B

$D\subseteq M\subseteq A \subseteq S$

C

$S\subseteq A$ and $M\subseteq D$

D

$S\subseteq A\subseteq M$ and $D\subseteq M$

E

$S\subseteq A$, $S\subseteq M$, and $D\subseteq M$

F

None of the above.