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Identify the smallest subset of $\mathbb{Z}$ containing $\{0,5,7\}$ closed under addition.

A

$\mathbb{Z}$

B

$35\mathbb{Z}$

C

$\mathbb{Z}_{\geq 0}\}$

D

$\{x\in \mathbb{Z}:x=5m+7n \textrm{ where } m,n\in\mathbb{Z}_{\geq 0}\}$

E

None of the above.

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