Consider the schema R = {S, T, U, V} and the dependencies S → T, T → U, U → V and V → S If R = (\(R_{1}\) and \(R_{2}\)) be a decomposition such that \(R_{1} \cap R_{2} = \phi\) then the decomposition is
in both 2NF and 3NF
The dependencies form a cycle S → T → U → V → S, so each single attribute determines all others and every attribute is a candidate key.
Any relation built from these attributes therefore has only prime attributes and every determinant is a key, so no partial or transitive dependency on a non-prime attribute can exist.
Hence each component of the decomposition satisfies 2NF and also 3NF (in fact BCNF), even though a disjoint split is not lossless.
3NF always implies 2NF, so 'in 3NF but not in 2NF' is impossible.
Hence, in both 2NF and 3NF.
Similar Questions
Which of the following is false ?
The Relation
Vendor Order (V_no, V_ord_no, V_name, Qty_sup, unit_price)
is in 2NF because :
Select the ‘False’ statement from the following statements about Normal Forms :
Consider the following relational schemas for a library database :
Book (Title, Author, Catalog_no, Publisher, Year, Price)
Collection(Title, Author, Catalog_no)
with the following functional dependencies :
I. Title, Author → Catalog_no
II. Catalog_no → Title, Author, Publisher, Year
III. Publisher, Title, Year → Price
Assume (Author, Title) is the key for both schemas. Which one of the following is true ?
Which of the following statements is false ?
In a schema R(A, B, C, D, E, F, G, H), each field of R contains only atomic values.
F = {CH→G, A→BC, B→CFH, E→A, F→EG} is a set of functional dependencies so that F+ is exactly the set of FDs that holds R. The relation R is :
Which of the following relations can not be decomposed in to BCNF with a lossless join and dependency-preserving decomposition ?
Which of the following/s is/are FALSE statement?
A. An all key relation is always in BCNF since it has no FDs.
B. A relation that is not in 4NF due to nontrivial MVD must be decomposed to convert it into a set of relations in 4NF.
C. The decomposition removes the redundancy by the MVD.
D. 3NF is stronger than BCNF.
Choose the correct answer from the options given below:
Fifth normal form is concerned with :
For a database relation R(A, B, C, D) where the domains of A, B, C and D include only atomic values, only the following functional dependencies and those that can be inferred from them are :
A → C
B → D
The relation R is in _______.
Important Questions from Normal Form
Which of the following statement(s) is/are correct regarding a relation in second normal form?
I. It is in first normal form
II. Every non-key attribute is fully and functionally independent on the primary key
Which of the following normal forms specifically addresses and eliminates partial dependencies?
Consider a relational schema team(name, city, owner), with functional dependencies {name $\to$ city, name $\to$ owner}.
The relation team is decomposed into two relations, t1(name, city) and t2(name, owner). Which of the following statement(s) is/are TRUE?
In a relational database, which one of the following is CORRECT:
Which of the following is false ?
