Dependency Preserving Decomposition?

Question

I am working on a textbook question and it asks the following:

Let R(A,B,C,D,E) be decomposed into relations with the following three sets of attributes: 

{A,B,C} , {B,C,D}, {A,C,E}

For each of the following sets of functional dependencies, determine if the dependencies 
are preserved by the decomposition.

**Functional Dependencies:** 

AC -> E and BC -> D

I am not sure how to solve this, and the textbook doesn't provide a clear enough explanation on dependency preserving. Can someone please explain how to do this? Thank you in advance.

Answer 1

R = {A,B,C,D,E} decomposed into R ₁ ={A,B,C} , R ₂ ={B,C,D} and R ₃ ={A,C,E}.

"determine if the dependencies are preserved by the decomposition."

Yes they are as BC->D is preserved in R ₂ and AC->E is preserved in R ₃ as is very apparent!
Note - Although a decomposition may be dependency-preserving it is not necessary that it is in a higher normal form.

There is an easy method to check whether a decomposition is dependency-preserving. Check this video.