16. PGT Computer Science Question Discussion

Let R (A, B, C, D) be a relational schema with the following functional dependencies:

A → B, B → C,
C → D and D → B. 

The decomposition of R into 
(A, B), (B, C), (B, D)

(A) gives a lossless join, and is dependency preserving
(B) gives a lossless join, but is not dependency preserving
(C) does not give a lossless join, but is dependency preserving
(D) does not give a lossless join and is not dependency preserving

(A,B) (B,C) −− common attribute is B and due to B→C, B is a key for (B,C)and hence ABC can be lossless decomposed into (A,B)and (B,C).

(A,B,C)(B,D), common attribute is B and B→D is a FD (via B→C,C→D), and hence, B is a key for (B,D). So, decomposition of (A,B,C,D)into (A,B,C)(B,D) is lossless.

Thus the given decomposition is lossless.

The given decomposition is also dependency preserving as the dependencies A→B is present in (A,B),B→C is present in (B,C),D→B is present in (B,D) and C→D is indirectly present via C→B in (B,C) and B→D in (B,D)


Sp Option (A) is correct