Which of the following statement is false?a)Relation with every attribute is prime always in 3NF.b)Relation with every candidate key simple always in 2NF.c)Relation with every attribute is prime always in BCNF.d)Relation R which satisfies 3NF and at most one compound candidate key is also in BCNF.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Normalization is used to minimize redundancy from a set of relations. It is used to organize data effectively in the database. Normal forms are used to reduce redundancy from the database.

Third Normal form: A relation is said to be in third normal form if it is in 2NF & there must not exist any transition dependency.

Also, it must satisfy these properties:

1. For the function A → B, A should be a super key.

2. B should be a part of a key attribute or prime attribute i.e. B should be a part of a candidate key.

BCNF: A relation is said to be in Boyce-Codd normal form (BCNF) if it is in 3NF & must satisfy this property:

1. For the function A → B, A should be a super key.

Assume a relation R(ABC) with the following functional dependencies:

A(ABC)

{AB → C,C → A}

Candidate keys are AB and BC.

AB → C is in BCNF but C → A not in BCNF.

So, the statement which is false is "Relation with every attribute is prime always in BCNF".

Hence, the correct option is (C).

Answer

The false statement is option 'C': Relation with every attribute is prime always in BCNF.

Explanation:
1. 3NF and Prime Attributes:
In a relation, if every non-prime attribute is functionally dependent on every candidate key, then it is in third normal form (3NF). Prime attributes are those attributes that are part of any candidate key. Therefore, in a relation that satisfies 3NF, every attribute is prime.

2. 2NF and Simple Candidate Keys:
In a relation, if every non-prime attribute is functionally dependent on the entire set of attributes of any candidate key, then it is in second normal form (2NF). Simple candidate keys are those candidate keys that consist of a single attribute. Therefore, in a relation that satisfies 2NF, every candidate key is simple.

3. BCNF and Non-prime Attributes:
BCNF (Boyce-Codd Normal Form) is a higher level of normalization than 3NF. In a relation, if every non-trivial functional dependency (dependency where the determinant is not a superkey) has a superkey as its determinant, then it is in BCNF. BCNF eliminates all redundancy, even beyond 3NF.

4. False Statement:
The false statement is option 'C' because not every attribute in a relation that satisfies BCNF is necessarily prime. In BCNF, the focus is on the functional dependencies and the determinants of these dependencies. The non-prime attributes can also be part of a functional dependency as long as the determinant is a superkey. Therefore, there can be non-prime attributes in a relation that satisfies BCNF.

5. Example:
Consider a relation R(A, B, C, D) with functional dependencies:
- A → B (A determines B)
- B → C (B determines C)
- C → D (C determines D)
- B → D (B determines D)

In this example, the candidate keys are {A} and {B}. Both A and B are prime attributes. However, D is a non-prime attribute. The relation R satisfies 3NF because every non-prime attribute is functionally dependent on the candidate keys. It also satisfies BCNF because every functional dependency has a superkey as its determinant. However, the false statement in option 'C' implies that every attribute in a relation that satisfies BCNF is always prime, which is not true in this example.

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