Number Theory

Free Version

Upgrade subject to access all content

Moderate

Containment with respect to $\mathbb{Z}$

NUMTH-KLJS6F

Which of the following statements are true?

A

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

B

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

C

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

D

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