Question 17100 – NTA UGC NET JUNE-2023 Paper-2

The decomposition of a relational schema R into smaller schemas can be analyzed for lossless join and dependency preservation using the properties of functional dependencies. Let’s break down the given functional dependencies:

A -> B
B -> C
C -> D
D -> B
Now, let’s consider the decomposition of R into (A, B), (B, C), and (B, D).

Lossless Join:
For the decomposition to be lossless join, we need to check if the natural join of the decomposed schemas can reconstruct the original relation R.

(A, B) ∩ (B, C) = (B)
(B, C) ∩ (B, D) = (B)
Both intersections include the attribute B. So, joining (A, B), (B, C), and (B, D) together would reconstruct all attributes of R. Therefore, the decomposition gives a lossless join.

Dependency Preservation:
For the decomposition to be dependency preserving, it should be checked if all the original functional dependencies can be inferred from the functional dependencies in the decomposed schemas.

In (A, B):

A -> B (from the original dependencies)
In (B, C):

B -> C (from the original dependencies)
In (B, D):

D -> B (from the original dependencies)
All original functional dependencies can be inferred from the functional dependencies in the decomposed schemas. Therefore, the decomposition is dependency preserving.

So, the correct answer is:

The decomposition gives a lossless join and is dependency preserving.