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A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPGE, ENDPAGE, TITLE, YEAR, PRICE)
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema.
The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE (VOLUME, NUMBER) -> YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> PRICE
The database is redesigned to use the following schemas.
The database is redesigned to use the following schemas.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR)
Q. Which is the weakest normal form that the new database satisfies, but the old one does not?
- a)1NF
- b)2NF
- c)3NF
- d)BCNF
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A database of research articles in a journal uses the following schema...
Volume, Number -> Year is partial dependency. So it does not follow 2NF. But decomposed relation follows.
Most Upvoted Answer
A database of research articles in a journal uses the following schema...
Explanation:
To determine the weakest normal form that the new database satisfies but the old one does not, we need to analyze the functional dependencies in both schemas and compare their normal forms.
Old Schema:
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE
- Functional Dependency: (VOLUME, NUMBER) -> YEAR
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> PRICE
New Schema:
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE
- Functional Dependency: (VOLUME, NUMBER) -> YEAR
1NF (First Normal Form):
- In 1NF, each attribute in a relation must have atomic values (no multi-valued attributes or repeating groups).
- Both the old and new schemas satisfy 1NF as there are no multi-valued attributes or repeating groups.
2NF (Second Normal Form):
- In 2NF, a relation must be in 1NF and every non-key attribute must be functionally dependent on the entire primary key.
- In the old schema, the attribute PRICE is not functionally dependent on the entire primary key (VOLUME, NUMBER, STARTPAGE, ENDPAGE). Therefore, the old schema does not satisfy 2NF.
- In the new schema, all attributes are functionally dependent on the entire primary key. Therefore, the new schema satisfies 2NF.
3NF (Third Normal Form):
- In 3NF, a relation must be in 2NF and every non-key attribute must be non-transitively dependent on the entire primary key.
- The old schema does not satisfy 2NF, so it also does not satisfy 3NF.
- The new schema satisfies 2NF, but we cannot determine if it satisfies 3NF based on the given functional dependencies.
BCNF (Boyce-Codd Normal Form):
- BCNF is a stronger version of 3NF where every determinant in a relation is a candidate key.
- Both the old and new schemas have functional dependencies where the determinants are not candidate keys (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and (VOLUME, NUMBER). Therefore, neither schema satisfies BCNF.
Weakest Normal Form:
- From the above analysis, we can conclude that the old schema does not satisfy 2NF, while the new schema satisfies 2NF. Therefore, the weakest normal form that the new database satisfies but the old one does not is 2NF (Second Normal Form).
To determine the weakest normal form that the new database satisfies but the old one does not, we need to analyze the functional dependencies in both schemas and compare their normal forms.
Old Schema:
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE
- Functional Dependency: (VOLUME, NUMBER) -> YEAR
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> PRICE
New Schema:
- Functional Dependency: (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE
- Functional Dependency: (VOLUME, NUMBER) -> YEAR
1NF (First Normal Form):
- In 1NF, each attribute in a relation must have atomic values (no multi-valued attributes or repeating groups).
- Both the old and new schemas satisfy 1NF as there are no multi-valued attributes or repeating groups.
2NF (Second Normal Form):
- In 2NF, a relation must be in 1NF and every non-key attribute must be functionally dependent on the entire primary key.
- In the old schema, the attribute PRICE is not functionally dependent on the entire primary key (VOLUME, NUMBER, STARTPAGE, ENDPAGE). Therefore, the old schema does not satisfy 2NF.
- In the new schema, all attributes are functionally dependent on the entire primary key. Therefore, the new schema satisfies 2NF.
3NF (Third Normal Form):
- In 3NF, a relation must be in 2NF and every non-key attribute must be non-transitively dependent on the entire primary key.
- The old schema does not satisfy 2NF, so it also does not satisfy 3NF.
- The new schema satisfies 2NF, but we cannot determine if it satisfies 3NF based on the given functional dependencies.
BCNF (Boyce-Codd Normal Form):
- BCNF is a stronger version of 3NF where every determinant in a relation is a candidate key.
- Both the old and new schemas have functional dependencies where the determinants are not candidate keys (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and (VOLUME, NUMBER). Therefore, neither schema satisfies BCNF.
Weakest Normal Form:
- From the above analysis, we can conclude that the old schema does not satisfy 2NF, while the new schema satisfies 2NF. Therefore, the weakest normal form that the new database satisfies but the old one does not is 2NF (Second Normal Form).
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A database of research articles in a journal uses the following schema.(VOLUME, NUMBER, STARTPGE, ENDPAGE, TITLE, YEAR, PRICE)The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema.(VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> TITLE (VOLUME, NUMBER) -> YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) -> PRICEThe database is redesigned to use the following schemas.(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR)Q.Which is the weakest normal form that the new database satisfies, but the old one does not?a)1NFb)2NFc)3NFd)BCNFCorrect answer is option 'B'. Can you explain this answer?
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