8. Let $[x]$ denote the greatest integer not exceeding $x$. If the set $S=\{(x, y)||[x+y]|+|[x-y] \mid \leqslant 1\}$, then the area of the plane region represented by the set $S$ is
A. $\frac{5}{2}$
B. 3
C. $\frac{9}{2}$
D. 4
Solve:
As shown in the figure, (1) $\left\{\begin{array}{l}{[x+y]=1,} \\ {[x-y]=0}\end{array}\right.$ or (2) $\left\{\begin{array}{l}{[x+y]=-1,} \\ {[x-y]=0}\end{array}\right.$
or (3) $\left\{\begin{array}{l}{[x+y]=0,} \\ {[x-y]=0}\end{array}\right.$ or (4) $\left\{\begin{array}{l}{[x+y]=0,} \\ {[x-y]=1}\end{array}\right.$
or (5) $\left\{\begin{array}{l}{[x+y]=0,} \\ {[x-y]=-1 .}\end{array}\right.$, and the area of each small square is $\frac{1}{2}$,
that is, the area of the plane region represented by the set $S$ is $\frac{5}{2}$, so the answer is $A$.