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Which of the following statements are true?

$\mathbb{Z} \subset \mathbb{Z} + \mathbb{Z}$, where $A + B = \{ a + b ~|~ a \in A, b \in B\}$.

$\mathbb{Z} + \mathbb{Z} \subset \mathbb{Z}$

$\mathbb{Z} + \mathbb{Z} \subset 2\mathbb{Z}$, where $2\mathbb{Z} = \{ 2n ~|~ n \in \mathbb{Z} \}$.

$\mathbb{Z} \subset \mathbb{Z} - \mathbb{Z}$, where $A - B = \{ a - b | a \in A, b \in B\}$