Question

What are all the nontrivial functional dependencies that follow from the given functional dependencies? You should restrict yourself to functional dependencies with single attributes on the right side.

Answer 1

Nontrivial functional dependencies are derived from a set of known dependencies and involve attributes that are not present on one side of the dependency. The Armstrong's axioms such as transitivity and augmentation are used to deduce these dependencies, which are crucial for database normalization.

Step-by-step explanation:

The question relates to functional dependencies within the context of databases and normalization. Nontrivial functional dependencies are derived from a given set without the entire set of attributes being present on one side of the dependency.

These can be deduced using Armstrong's axioms, which are a set of rules used to infer all the functional dependencies on a database given a set of known dependencies.

A functional dependency is considered nontrivial if the right-side attribute is not a subset of the left-side. When deciphering nontrivial functional dependencies from a given set, we use three main rules: transitivity, augmentation, and reflexivity to generate all possible functional dependencies.

For instance, if we have a dependency A -> B, and we know that B -> C, through transitivity we can deduce that A -> C is also a nontrivial functional dependency.

Similarly, if we add an attribute to both sides of a dependency, like turning A -> B into AY -> BY by augmentation, we can infer new dependencies. To find all nontrivial functional dependencies, we systematically apply these rules.