4.9 If $b<c$ and $1<a<b+c<a+1$, then
(A) $a<b$.
(B) $a=b$.
(C) $a \leqslant b$.
(D) $b<a$.
(Chinese Jiangsu Province Junior High School Mathematics Competition, 1990)
[Solution] If $b \geqslant a$, then by $c>b$, we have $c>a$, $\therefore \quad b+c>2 a$.
Also, $b+c>1$ contradicts.
Therefore, $a>b$.
Hence, the correct choice is $(D)$.