Which of the following are (recursive) definitions of the set of integers \(\mathbb{Z}\)? (Select True/False for each one.)

1. \[\begin{array}{ll} \textrm{Basis Step: } & 5 \in \mathbb{Z} \\ \textrm{Recursive Step: } & \textrm{If } x \in \mathbb{Z} \textrm{, then } x+1 \in \mathbb{Z} \textrm{ and } x-1 \in \mathbb{Z} \end{array}\]

2. \[\begin{array}{ll} \textrm{Basis Step: } & 0 \in \mathbb{Z} \\ \textrm{Recursive Step: } & \textrm{If } x \in \mathbb{Z} \textrm{, then } x+1 \in \mathbb{Z} \textrm{ and } x-1 \in \mathbb{Z} \textrm{ and } x+2 \in \mathbb{Z} \textrm{ and } x-2 \in \mathbb{Z} \end{array}\]

3. \[\begin{array}{ll} \textrm{Basis Step: } & 0 \in \mathbb{Z} \\ \textrm{Recursive Step: } & \textrm{If } x \in \mathbb{Z} \textrm{, then } x+2 \in \mathbb{Z} \textrm{ and } x-1 \in \mathbb{Z} \end{array}\]

4. \[\begin{array}{ll} \textrm{Basis Step: } & 0 \in \mathbb{Z} \\ \textrm{Recursive Step: } & \textrm{If } x \in \mathbb{Z} \textrm{, then } x+1 \in \mathbb{Z} \textrm{ and } x+2 \in \mathbb{Z} \end{array}\]