Question

Consider R(A, B, C, D, E) be a relation schema with the following functional dependencies:

$F=\{A\to BC,CD\to E,B\to D,E\to A\}$

Which of the following is true for decomposition of R into (A, B, C) and (C, D, E)?

• A. Lossless join and dependency preserving.
• B. Not lossless join but dependency preserving
• C. Neither lossless join nor dependency preserving.
• D. Lossless join but not dependency preserving

Answer 1

The correct option is C Neither lossless join nor dependency preserving.

(a)
$R_1\left(ABC\right)\cap R_2\left(CDE\right)=C$
But C is not the super key of neither relation
$R_1\text{nor relation}{R}_2$.
So it is lossy decomposition.

$E\to AandB\to D\text{are not preserving in decomposing}$.

Hence it is not dependency preserving.