[Solution] Consider the set $\{-3,0,3\}$ satisfies conditions (1) - (4), then (B), (C), (D) cannot be true.
Therefore, the answer is $(A)$.
15.19 A set $P$ with certain integers as elements has the following properties:
(1) $P$ contains positive and negative numbers;
(2) $P$ contains odd and even numbers;
(3) $-1 \notin P$; (4) If $x, y \in P$, then $x+y \in P$. For this set $P$, it can be concluded that
(A) $0 \in P, 2 \notin P$.
(B) $0 \notin P, 2 \in P$.
(C) $0 \in P, 2 \in P$.
(D) $0 \notin P, 2 \notin P$.
（1st “Hope Cup” National Mathematics Invitational Competition, 1990）