Lossy OR Lossless Decomposition

Question

Consider the relation R(A,B,C,D,E) with the set of F=(A->C,B->C,C->D,DC->C,CE->A) Suppose the relation has been Decomposed by the relations R1(A,D),R2(A,B),R3(B,E),R4(C,D,E),R5(A,E)

Is this decomposition lossy or lossless?

i tried solving this question using the matrix method and i am getting the answer as lossless because i managed to get a row in the 5*5 matrix filled with one variable however the book from which i am solving gives the answer as lossy. which one is the correct answer??

Answer 1

It is a lossless decomposition for sure. The row corresponding to R ₃ gets filled with one variable.

As an aside , if you have the above decomposition obtained using Bernstein Synthesis then just checking whether any of the decomposed relations consists of all the attributes of the key of the original relation R will ensure that it's a lossless decomposition. For example, BE is the key for the relation R in the example above. The decomposed relation R ₃ consists of both the primary attributes B and E and hence this ensures a lossless decomposition.