1. The set $P$ consisting of certain integers has the following properties:
(1) $P$ contains both positive and negative numbers;
(2) $P$ contains both odd and even numbers;
(3) $-1 \notin P$;
(4) If $x, y \in P$, then $x+y \in P$.

Determine the relationship between the numbers $0$ and $2$ and the set $P$.
1. From (4), we know that if $x \in P$, then $k x \in P(k \in \mathrm{N})$. From (1), we can assume $x, y \in P$, and $x>0, y$ $2 n-1$, then the negative odd number $-2 q m+(2 n-1) \in P$, which is a contradiction. Therefore, $2 \in P$.