IS5413 Chap.7 Functional Dependencies and Normal Forms
Functional Dependencies and Normal Forms
The dependency set is the deliverable, not the working
A functional dependency holds when knowing one attribute, called the determinant, settles what another must be. Normalisation is defined by the course as the process of decomposing relations that show anomalies into smaller well structured relations, and its entire input is the dependency set.
This is the step candidates skip, and skipping it is precisely why the decomposition that follows has to be guessed.
The published course objectives name analysing functional dependencies as a goal in its own right, the design question asks for them as a separate deliverable, and the group project brief requires them to be shown in the relations before third normal form can be demonstrated.
Anomalies are the symptom; dependencies are the cause
A well structured relation is one with minimal redundancy in which rows can be inserted, deleted and updated without creating inconsistencies.
Three named anomalies show the definition being broken. An insertion anomaly means a new fact cannot be recorded without inventing an unrelated one. A deletion anomaly means removing one fact silently destroys another. A modification anomaly means one real world change has to be written to many rows.
All three have the same root cause, which the course states plainly: the table covers more than one theme, so an unnecessary dependency exists between things that are not really connected.
Anomalies are how you notice there is a problem; the dependencies are what tell you where to cut.
The ladder, and the shortcut that saves time
First normal form requires no multivalued attributes and atomic values, and every relation is already in it by definition. Second normal form adds that each non key attribute depends on the key as a whole rather than on a piece of it.
Third normal form adds that no transitive dependency remains, meaning no non key attribute determines another non key attribute. The shortcut worth remembering is that partial dependencies require a composite key to exist at all: a relation in first normal form with a single attribute key is automatically in second normal form.
Transitive dependencies can appear under any key, so a relation with a tidy single column key still has to be checked. Beyond third normal form sit Boyce Codd, fourth and fifth, and the course states that third is generally considered sufficient.
What a decomposition must preserve
Each split should be reported with the dependency that forced it, because that sentence is what makes the answer checkable.
The other thing to watch is the join back. When a non key determinant moves out to become the key of a new relation, it stays behind in the original as a foreign key; dropping it instead loses the ability to reconstruct the original row, which is data loss rather than normalisation.
Finally, normalisation and physical design pull in opposite directions on purpose: normalise fully at the logical level so that the correct structure is known, then denormalise specific relations at the physical level with a stated reason and a known cost.
What this chapter covers
- 01
Determinants and the dependency set
- 02
Insertion, deletion and modification anomalies
- 03
Partial dependencies and why they need a composite key
- 04
Transitive dependencies under any key
- 05
First, second and third normal form
- 06
Reporting the dependency that forced each split
- 07
Why the determinant stays behind as a foreign key
Worked example · free
Produce the dependency set, then the decomposition
- 2State the primary key and justify it from the narrative.
- 4Write every functional dependency with the determinant on the left.
- 2Name the normal form and the dependency type that caps it.
- 4Give the resulting relations and name the dependency that forced each split.
Key terms
- Functional Dependency
- A constraint under which knowing one attribute, the determinant, settles another. Written with the determinant on the left of the arrow.
- Determinant
- The attribute or combination of attributes on the left of a functional dependency, whose value settles the value on the right.
- Partial Dependency
- A dependency in which a non key attribute is determined by only part of a composite primary key. It cannot exist where the key is a single attribute.
- Transitive Dependency
- A dependency in which a non key attribute determines another non key attribute, so that the key fixes the first which fixes the second.
- Insertion Anomaly
- The situation in which a new fact cannot be recorded without supplying an unrelated one, because two themes share a single relation.
- Well Structured Relation
- A relation with minimal redundancy in which rows can be inserted, deleted and updated without producing inconsistencies.
- Boyce Codd Normal Form
- The level above third normal form, which removes the anomalies that remain when a relation has several overlapping candidate keys.
Functional Dependencies and Normal Forms FAQ
How do I know when to stop normalising?
The course states that third normal form is generally considered sufficient, and the group project brief asks for third normal form specifically. Boyce Codd, fourth and fifth normal form exist above it and address anomalies arising from multiple candidate keys and from multivalued dependencies. Unless a question supplies a reason to go further, reaching third normal form and saying that you have is the complete answer.
Why is my relation already in second normal form?
Most likely because its primary key is a single attribute. A partial dependency is by definition a dependency on part of the key, so a key with no parts cannot have one, and a relation in first normal form with a simple key is in second normal form automatically. Saying that explicitly is worth a mark, because it demonstrates that you know why rather than merely that.
What is the most common way to lose marks on a normalisation question?
Writing the dependency set as a restatement of the schema, with the key on the left and every other attribute on the right. That hides exactly the partial dependencies the question is about and makes the decomposition unverifiable. The next two are splitting without naming the dependency that forced the split, and dropping the determinant from the original relation after moving it, which loses the join back.
Exam move
Take five relations from any source and do only the dependency set for each, on paper, before deciding a normal form. Then decide the form and write one sentence per split naming the dependency responsible. Finish with the check that catches almost everything: read each non key column in turn and ask what determines it, because if the answer is another non key column the relation is not yet in third normal form.
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