8. Let $[x]$ denote the greatest integer not exceeding the real number $x$. If the set
$$
S=\{(x, y)||[x+y]|+|[x-y] \mid \leqslant 1\},
$$
then the area of the plane region represented by $S$ is ( ).
(A) $\frac{5}{2}$
(B) 3
(C) $\frac{9}{2}$
(D) 4
8. A.
(1) When $0 \leqslant x+y<1$, $[x+y]=0$, then $|[x-y]| \leqslant 1 \Rightarrow -1 \leqslant x-y<2$;
(2) When $1 \leqslant x+y<2$, $[x+y]=1$, then $|[x-y]|=0 \Rightarrow 0 \leqslant x-y<1$;
(3) When $-1 \leqslant x+y<0$, $[x+y]=-1$, then $|[x-y]|=0 \Rightarrow 0 \leqslant x-y<1$.
By plotting the regions that satisfy the above conditions, we find that the required area is $\frac{5}{2}$.