子架构中不显示使用功能依赖项保留依赖项的分解

我在读一本教科书,里面有以下问题:

Given the following relation R {A,B,C,D,E,H} and the functional 
dependencies AB->CD, BC->D, C->H, D->HB, CH->AE
does the following decomposition is dependency preserving?
R1(A,C,E,H) R2(B,D,H), R3(A,B,C), R4(B,C,D)

教科书的答案是,它实际上是功能依赖保持,我认为这不是因为依赖 AB->D
Reading this answer 使它更加混乱,因为它使它看起来像
if there is a key inside one of the sub relations, the decomposition must be dependency preserving
我不能反驳的一个反例是
For the two rows a1 b1 c1 d1 h1 e2 and a2 b1 c2 d2 h2 e2
R的所有F.D保持不变,但现在r3已经
a1 b1 c1 and a2 b1 c2
和R4有 b1 c1 d1 and b1 c2 d2 ,
将r3和r4连接到b上给出 a1 b1 c2 d2 它打破了 AB & GT FD