BCNF Decomposition: Confusion regarding given answer

Question

I encountered the following question:

Given a relation R(A, B, C, D) with the following functional dependencies:
A -> B, C -> D, B -> C.

The BCNF Decomposition of R is:

A) {(A,B), (C,D), (B,C)}
B) {(A,B), (C,D), (A,C)}
C) {(B,C), (A,D), (A,B)}
D) All of the above

According to my understanding the solution should be D) ALL of the above.
This is because for each schema, the condition for BCNF holds as given by this link: http://www.cs.sfu.ca/CourseCentral/354/jpei/slides/UsingBCNF-3NF.pdf (Page 18)

The other two do not preserve some dependencies but in BCNF decomposition it may happen that the dependencies are not preserved.

However, the answer is given as (A). Please can someone explain? Thanks.