Example 9 Let $a$ be a rational number. Among the following four conclusions, the correct one is ( ).
(A) $[a]+[-a]=0$
(B) $[a]+[-a]$ equals 0 or 1
(C) $[a]+[-a] \neq 0$
(D) $[a]+[-a]$ equals 0 or -1
(17th "Hope Cup" Mathematics Invitational (Grade 7))
(1) If $a$ is an integer, then $[a]=a$, and
$[-a]=-a$.
Therefore, $[a]+[-a]=a+(-a)=0$.
(2) If $a$ is not an integer, then $a-1<[a]<a$, and $-a-1<[-a]<-a$.
Therefore, $-2<[a]+[-a]<0$.
Thus, $[a]+[-a]=-1$.
Combining (1) and (2), the correct choice is (D).
[Note] The above solution uses the method of case analysis to provide a rigorous solution to this problem, proving that “$[a]+[-a]$ equals 0 or -1”. Since this is a multiple-choice question, special value method or elimination method can also be used to answer.