GATE CSE 1990 Question on Third Normal Form (3NF) & Functional Dependencies
This post explores the concepts of Third Normal Form (3NF) in relational databases and the types of functional dependencies that may still exist in a 3NF database. We provide a detailed discussion to help you master these crucial concepts for GATE CSE.
Original GATE Question
Year: 1990
Topic: Relational Database Normalization
Question: What types of undesirable data redundancy may still exist in a relational database in Third Normal Form (3NF)?
Detailed Solution
To answer this question, let’s first break down what 3NF means and the types of functional dependencies that can exist in a 3NF database.
What is Third Normal Form (3NF)?
Third Normal Form (3NF) is a level of database normalization that eliminates transitive dependencies in a relation. Specifically, a relation is in 3NF if:
- It is in Second Normal Form (2NF).
- No non-prime attribute is transitively dependent on any candidate key. A transitive dependency means that an attribute indirectly depends on a key through another attribute.
Types of Functional Dependencies in 3NF
In 3NF, while most redundancies are removed, some types of undesirable functional dependencies may still exist, including:
- Transitive Functional Dependencies: These occur when an attribute is indirectly dependent on a primary key through another attribute.
- Non-trivial Functional Dependencies: These involve attributes that are not part of the candidate keys, which still cause redundancy.
Analyzing the Options
The question lists several types of functional dependencies that may cause undesirable data redundancy in a 3NF database:
- Option A: Transitive functional dependencies – Correct. Even in 3NF, transitive dependencies involving non-prime attributes can exist.
- Option B: Non-trivial functional dependencies involving prime attributes on the right-side – Correct. This type of functional dependency can still cause redundancy.
- Option C: Non-trivial functional dependencies involving prime attributes only on the left-side – Incorrect. In 3NF, such functional dependencies are not problematic, and if all dependencies involve prime attributes on the left, the relation would be in BCNF.
- Option D: Non-trivial functional dependencies involving only prime attributes – Correct. These can exist in a 3NF database and may cause some degree of redundancy.
Common Misconceptions about 3NF
A common misconception is that a 3NF database is free of all redundancy. While it is true that 3NF eliminates transitive dependencies on non-prime attributes, it can still contain functional dependencies on prime attributes, which may lead to data redundancy.
Correct Answer
The correct answer to this GATE 1990 question is A, B, and D, indicating that a 3NF database may still have undesirable data redundancy due to:
- Transitive functional dependencies (Option A),
- Non-trivial functional dependencies involving prime attributes on the right-side (Option B),
- Non-trivial functional dependencies involving only prime attributes (Option D).
Solution Summary
- Third Normal Form (3NF): A relation is in 3NF if it is in 2NF and no non-prime attribute is transitively dependent on any candidate key.
- Redundancies in 3NF: While 3NF removes most redundancies, transitive and non-trivial functional dependencies may still exist, particularly those involving prime attributes.
Common Student Doubts (FAQs)
Q1: Can a 3NF database have transitive dependencies?
A: Yes, a 3NF database can have transitive dependencies, but only involving prime attributes.
Q2: Why is a relation in 3NF not completely free of redundancy?
A: In 3NF, non-trivial dependencies involving prime attributes may still cause redundancy, unlike in Boyce-Codd Normal Form (BCNF), which eliminates such redundancies.
Q3: Does 3NF eliminate all types of functional dependencies?
A: No, 3NF focuses on eliminating transitive dependencies on non-prime attributes but may still allow dependencies involving prime attributes.
