Hi all,

Lets say we have the relation R(A,B,C,D)

with the following function dependencies:

A, B -> C

B -> A

and we decompose R as follows:

R1( A,B) - Is in BCNF with superkey {B} and the FD B -> A holds in it.

R2(B, C, D).

My questions are:

1. Does the FD A,B -> C holds in R1?

2. Does the FD B->C holds in R2?

As a follow-up question to both, if the answer is yes, is it because of transitivity in the original set of FDs where B->A (B -> A, B -> C => B -> C holds in R) or is it because we have R2 in which B->A holds? If the answer is no, does it mean we lost that FD?

Thanks