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 _______.
First normal form but not in second normal form.
First normal form needs only atomic domains. Second normal form additionally forbids partial dependencies, i.e. a non-prime attribute depending on a proper part of a candidate key. Third normal form further forbids transitive dependencies of non-prime attributes on a candidate key.
Step 1 — Closures: \(\{A\}^+ = \{A, C\}\), \(\{B\}^+ = \{B, D\}\) and \(\{A, B\}^+ = \{A, B, C, D\}\). Neither A nor B alone determines all attributes, so AB is the only candidate key; A and B are prime, C and D are non-prime.
Step 2 — All domains are atomic, so R is in first normal form.
Step 3 — A → C makes the non-prime attribute C depend on A, a proper subset of the candidate key AB; likewise B → D makes D depend only on B. These are partial dependencies, so R violates second normal form, and a relation not in second normal form cannot be in third normal form either.
Every choice that places R in second normal form, with or without third normal form, ignores these partial dependencies on the composite key.
First normal form but not in second normal form. option is correct.
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 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
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 :
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 ?
