Question

Given a relation ( R ) not in 3NF, a 3NF decomposition of ( R ) is always possible, but it might not be dependency preserving.

a. True
b. False

Answer 1

A relation (R) that is not in 3NF can always be decomposed into multiple smaller relations that are in 3NF, but this decomposition may not preserve all the functional dependencies that existed in the original relation.

Step-by-step explanation:

The statement is true. A relation (R) that is not in 3NF can always be decomposed into multiple smaller relations that are in 3NF, but this decomposition may not preserve all the functional dependencies that existed in the original relation.

3NF (Third Normal Form) is a level of database normalization that ensures elimination of redundancy and preserves dependencies between attributes. When decomposing a relation into smaller relations, we aim to eliminate transitive dependencies and create tables with a single purpose.

For example, let's say we have a relation (R) with attributes {A, B, C} and the functional dependencies {A -> B, B -> C}. This relation is not in 3NF because of the transitive dependency A -> C. However, we can decompose it into two relations, {A, B} and {B, C}, which are in 3NF but do not preserve the original dependency A -> C.