Match List I with List II: Choose the correct answer from the options given below:List I List II (A) BCNF (I) It removes multivalued dependency (B) 3 NF (II) It is not always dependency preserving (C) 2 NF (III) It removes transitive dependency (D) 4 NF (IV) It removes partial functional dependency
(A) - (II), (B) - (III), (C) - (IV), (D) - (I)
Understanding Database Normal Forms and Dependencies
Database normalization is a process used in relational database design to reduce data redundancy and improve data integrity. It involves organizing columns and tables to ensure that dependencies are properly enforced. Different normal forms (NF) address specific types of data anomalies and dependencies.
Let's analyze each normal form mentioned in List I and match it with its characteristic from List II:
- BCNF (Boyce-Codd Normal Form): BCNF is a stricter version of 3NF. A relation is in BCNF if for every non-trivial functional dependency $\text{X} \rightarrow \text{Y}$, $\text{X}$ is a superkey. While BCNF eliminates more redundancy than 3NF, the decomposition process to achieve BCNF is not always dependency preserving. This means that after decomposing a relation into BCNF, some original functional dependencies might not be inferable from the dependencies within the new relations. Therefore, BCNF is not always dependency preserving. This matches with characteristic (II).
- 3NF (Third Normal Form): A relation is in 3NF if it is in 2NF and there are no transitive dependencies. A transitive dependency exists when a non-prime attribute is dependent on another non-prime attribute, which in turn is dependent on the candidate key (e.g., $\text{A} \rightarrow \text{B}$ and $\text{B} \rightarrow \text{C}$, where $\text{A}$ is the key and $\text{B}$ and $\text{C}$ are non-prime attributes). 3NF specifically targets and removes this type of dependency by decomposing the relation. This matches with characteristic (III).
- 2NF (Second Normal Form): A relation is in 2NF if it is in 1NF and all non-prime attributes are fully functionally dependent on every candidate key. A partial functional dependency occurs when a non-prime attribute is dependent on only a part of a candidate key. 2NF aims to eliminate these partial functional dependencies by moving the partially dependent attributes to a new table. This matches with characteristic (IV).
- 4NF (Fourth Normal Form): A relation is in 4NF if it is in BCNF and contains no multivalued dependencies. A multivalued dependency ($\text{A} \rightarrow \rightarrow \text{B}$) exists when, for a value of A, there is a set of B values, and this set is independent of other attributes in the relation. 4NF removes multivalued dependencies that are not also functional dependencies by decomposing the relation. This matches with characteristic (I).
Matching List I with List II
Based on the analysis above, the correct matching is:
- (A) BCNF — (II) It is not always dependency preserving
- (B) 3 NF — (III) It removes transitive dependency
- (C) 2 NF — (IV) It removes partial functional dependency
- (D) 4 NF — (I) It removes multivalued dependency
| List I (Normal Form) | List II (Characteristic) | Match |
|---|---|---|
| (A) BCNF | (I) It removes multivalued dependency | (A) — (II) |
| (B) 3 NF | (II) It is not always dependency preserving | (B) — (III) |
| (C) 2 NF | (III) It removes transitive dependency | (C) — (IV) |
| (D) 4 NF | (IV) It removes partial functional dependency | (D) — (I) |
Revision Table: Normal Forms Summary
| Normal Form | Addresses | Dependency Type Removed |
|---|---|---|
| 1NF | Atomic values | Eliminates repeating groups |
| 2NF | Partial Dependency | Partial functional dependencies |
| 3NF | Transitive Dependency | Transitive functional dependencies |
| BCNF | Anomalies not covered by 3NF | Functional dependencies where determinant is not a superkey (stricter than 3NF) |
| 4NF | Multivalued Dependency | Multivalued dependencies |
Additional Information on Database Dependencies
Understanding the different types of dependencies is key to mastering database normalization.
- Functional Dependency ($\text{X} \rightarrow \text{Y}$): If the value of attribute set $\text{X}$ uniquely determines the value of attribute set $\text{Y}$ in a relation instance.
- Partial Dependency: A functional dependency $\text{X} \rightarrow \text{Y}$ where $\text{Y}$ is a non-prime attribute and $\text{X}$ is a proper subset of a candidate key.
- Transitive Dependency: A functional dependency $\text{X} \rightarrow \text{Z}$ that can be inferred via a set of dependencies $\text{X} \rightarrow \text{Y}$ and $\text{Y} \rightarrow \text{Z}$, where $\text{Y}$ is neither a superkey nor a subset of any candidate key of the relation, and $\text{Z}$ is a non-prime attribute.
- Multivalued Dependency ($\text{X} \rightarrow \rightarrow \text{Y}$): A constraint between two sets of attributes in a relation. For a relation $\text{R}(\text{A, B, C})$, $\text{A} \rightarrow \rightarrow \text{B}$ if whenever we have tuples $(\text{a, b}_1, \text{c}_1)$ and $(\text{a, b}_2, \text{c}_2)$ in $\text{R}$, we must also have $(\text{a, b}_1, \text{c}_2)$ and $(\text{a, b}_2, \text{c}_1)$ in $\text{R}$. This holds true for any $\text{c}_1, \text{c}_2$ and $\text{b}_1, \text{b}_2$. Essentially, the set of $\text{B}$ values associated with an $\text{A}$ value is independent of the $\text{C}$ values.
- Dependency Preservation: A decomposition is dependency preserving if all original functional dependencies can be enforced by checking functional dependencies only in the relations of the decomposition. 3NF decomposition is always dependency preserving, but BCNF decomposition is not always.
- Lossless Join Decomposition: A decomposition is lossless if joining the decomposed relations on their common attributes yields the original relation without generating spurious tuples. Both 3NF and BCNF decompositions can be performed losslessly.
Important Questions from Normal Form - Teaching
Consider a schema R(A, B, C, D) and following functional dependencies.
A → B
B → C
C → D
D → B
Then decomposition of R into R 1(A, B), R 2(B, C) and R 3(B, D) is _______
If every non-key attribute is functionally dependent on the primary key, then the relation is in _______.
Consider a relation R (A, B, C, D, E, F, G, H), where each attribute is atomic, and following functional dependencies exist.
CH → G
A → BC
B → CFH
E → A
F → EG
The relation R is ______.
For a database relation R(a, b, c, d) where the domains of a, b, c, and d include only atomic values, and only the following functional dependencies and those that can be inferred from them hold:
a → c
b → d
The relation is in.In relational database, if a relation R is in BCNF, then which of the following is true about relation R?
