Chapter 7, Problem 1PE

Explanation of Solution

Lossless decomposition:

A decomposition $\left\{\text{R1,R2}\right\}$ is known to be lossless join decomposition when the relation $\text{R1}\cap \text{R2}\to \text{R1}$ or $\text{R1}\cap \text{R2}\to \text{R2}$.

Using the given decomposed schemas:

Considering the decomposed schema to be:

$\begin{array}{l}\text{R1=}\left(\text{A,B,C}\right)\\ \text{R2=}\left(\text{A,D,E}\right)\end{array}$

Now,

$\text{R1}\cap \text{R2}\to \text{A}$

Here, A is considered to be the candidate key which can be implied to be that $\text{R1}\cap \text{R2}\to \text{R1}$ but not in the other way.

Therefore, the given decomposition is loss-less decomposition when A is considered to be the candidate key.