1. The condition $[x]=[y]$ is the condition $|x-y|<1$ ( )
A. Sufficient but not necessary condition
B. Necessary but not sufficient condition
C. Sufficient and necessary condition
D. Neither sufficient nor necessary condition
1. Let $a=[x]=[y]$, then $a \leqslant x, y < a+1$, naturally we have $|x-y|<1$. Conversely, take $x=-\frac{1}{3}, y=$ $\frac{1}{3}$, then $|x-y|<1$, but $[x] \neq [y]$.