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A relation 'R', in which every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, is said to be in
- a)1st normal form
- b)2nd normal form
- c)3rd normal form
- d)Boyce-Codd normal form
Correct answer is option 'B'. Can you explain this answer?
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A relation R, in which every attribute is functionally dependent on th...
1 NF - A relation R is in first normal form (1 NF) if and only if all underlying domains contain atomic values only.
2 NF - A relation R is in second normal form (2 NF) if and only if it is in 1 NF and every non-key attribute is fully dependent on the primary key.
3 NF - A relation R is in third normal form (3 NF) if and only if it is in 2 NF and every non-key attribute is non-transitively dependent on the primary key.
BCNF - A relation R is in Boyce-Codd normal form (BCNF) if and only if every determinant is a candidate key.
Example:
Consider a relation R(XYZ) with functional dependencies {X → Y, Y → Z, X → Z}.
This relation is in 2 NF but not in 3 NF because every non-key attribute is transitively dependent on the primary key. Here, {X} will be a candidate key.
So, option (2) is correct.
2 NF - A relation R is in second normal form (2 NF) if and only if it is in 1 NF and every non-key attribute is fully dependent on the primary key.
3 NF - A relation R is in third normal form (3 NF) if and only if it is in 2 NF and every non-key attribute is non-transitively dependent on the primary key.
BCNF - A relation R is in Boyce-Codd normal form (BCNF) if and only if every determinant is a candidate key.
Example:
Consider a relation R(XYZ) with functional dependencies {X → Y, Y → Z, X → Z}.
This relation is in 2 NF but not in 3 NF because every non-key attribute is transitively dependent on the primary key. Here, {X} will be a candidate key.
So, option (2) is correct.
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A relation R, in which every attribute is functionally dependent on th...
2nd Normal Form Explanation:
Firstly, it is important to understand the concept of normalization in database design. Normalization is a process of organizing data in a database to reduce redundancy and improve data integrity. There are several normal forms, and each form has specific criteria that must be met for a relation to be in that normal form.
Key Attributes and Functional Dependencies:
- In a relation, a key attribute uniquely identifies each tuple.
- Functional dependency means that the value of one attribute uniquely determines the value of another attribute in the same tuple.
- In 2nd normal form, every non-key attribute must be fully functionally dependent on the primary key. This means that all non-key attributes are dependent on the entire primary key, not just part of it.
Relation in 2nd Normal Form:
- A relation in 2nd normal form ensures that there are no partial dependencies, where a non-key attribute is dependent on only a part of the primary key.
- If every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, then the relation is said to be in 2nd normal form.
- This ensures data integrity and reduces redundancy in the database.
Therefore, in the given scenario where every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, the relation is in 2nd normal form.
Firstly, it is important to understand the concept of normalization in database design. Normalization is a process of organizing data in a database to reduce redundancy and improve data integrity. There are several normal forms, and each form has specific criteria that must be met for a relation to be in that normal form.
Key Attributes and Functional Dependencies:
- In a relation, a key attribute uniquely identifies each tuple.
- Functional dependency means that the value of one attribute uniquely determines the value of another attribute in the same tuple.
- In 2nd normal form, every non-key attribute must be fully functionally dependent on the primary key. This means that all non-key attributes are dependent on the entire primary key, not just part of it.
Relation in 2nd Normal Form:
- A relation in 2nd normal form ensures that there are no partial dependencies, where a non-key attribute is dependent on only a part of the primary key.
- If every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, then the relation is said to be in 2nd normal form.
- This ensures data integrity and reduces redundancy in the database.
Therefore, in the given scenario where every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, the relation is in 2nd normal form.
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A relation R, in which every attribute is functionally dependent on the key and every non-key attribute is fully dependent on the primary key, is said to be ina)1st normal formb)2nd normal formc)3rd normal formd)Boyce-Codd normal formCorrect answer is option 'B'. Can you explain this answer?
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