Chapter 7, Problem 29E

Explanation of Solution

To show the lossless decomposition:

• Given that (A,B,C), AND (C,D,E) are the decompositions of schema “R”.
• Consider the defined functional dependencies holds true.
• For functional dependencies refer Practice Exercises 7.1.
• To show the below example of relation “r”, follow the given hint.

A	B	C	D	E
a1	b1	c1	d1	e1
a2	b2	c1	d2	e2

• After the decomposition, ${\text{π}}_{\text{R1}}\left(\text{r}\right)$ will be as follows,

A	B	C
a1	b1	c1
a2	b2	c1

• ${\pi }_{\text{R2}}$ will be as follows,

C	D	E
c1	d1	e1
c1	d2