14. 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 0, 2 and the set $P$.
14. $0 \in P, 2 \notin P$.

Let $a$ be the smallest positive number in $P$, and $b$ be the largest negative number in $P$, then $b < a + b < a$, and $a + b \in P$, but $a + b$ is neither positive nor negative, thus $a + b = 0$, which means $0 \in P$;
Since $1 \notin P$, we have $a \geqslant 2$, and since $a + b = 0 \Rightarrow a = -b$, it follows that $b \leqslant -2$.
If $a = 2$, then $b = -2$, and repeatedly using condition (4), we get $\pm 2k \in P, k \in \mathbf{N}$. Since $P$ contains odd numbers, let $m = 2t + 1 \in P$, and combining with $-2t \in P$ we get $1 \in P$, which is a contradiction, hence $2 \notin P$.
In summary, $0 \in P$ and $2 \notin P$.