Im not sure when decomposition to BCNF loses functional dependencies. We have functional dependencies A_1, A_2, A_3 , and let's say that A_1, A_2 can be minimized to some dependency A_x then if decomposition holds A_x , but doesnt hold A_1, A_2 , did it "lose functional dependencies"? We have relation R = {A, B, C} with dependencies A -> B, B -> C now we decompose it to BCNF by creating R1 = {A, B} and R2 = {B, C} . If I understand correctly, we didnt "lose functional dependencies". However, if we added A -> BC to the dependencies then we would have lost it?

BCNF and losing functional dependencies

Im not sure when decomposition to BCNF loses functional dependencies.

We have functional dependencies A_1, A_2, A_3, and let's say that A_1, A_2 can be minimized to some dependency A_x then if decomposition holds A_x, but doesnt hold A_1, A_2, did it "lose functional dependencies"?
We have relation R = {A, B, C} with dependencies A -> B, B -> C now we decompose it to BCNF by creating R1 = {A, B} and R2 = {B, C}. If I understand correctly, we didnt "lose functional dependencies". However, if we added A -> BC to the dependencies then we would have lost it?