# Normal Form

 Question 1
Suppose the following functional dependencies hold on a relation U with attributes $P, Q, R, S, \text{ and } T$:

$P \rightarrow QR \\ RS \rightarrow T$

Which of the following functional dependencies can be inferred from the above functional dependencies?
[MSQ]
 A $PS \rightarrow T$ B $R \rightarrow T$ C $P \rightarrow R$ D $PS \rightarrow Q$
GATE CSE 2021 SET-2   Database Management System
Question 1 Explanation:
 Question 2
If every non-key attribute functionally dependent on the primary key, then the relation will be in
 A First normal form B Second normal form C Third normal form D Fourth Normal form
ISRO CSE 2020   Database Management System
Question 2 Explanation:
 Question 3
Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?
 A R has a nontrivial functional dependency $X\rightarrow A$, where X is not a superkey and A is a prime attribute. B R has a nontrivial functional dependency $X\rightarrow A$, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key. C R has a nontrivial functional dependency $X\rightarrow A$, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key. D A cell in R holds a set instead of an atomic value.
GATE CSE 2020   Database Management System
Question 3 Explanation:
 Question 4
Let the set of functional dependencies $F=\{QR\rightarrow S,R\rightarrow P,S\rightarrow Q\}$ hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z where Y = (PR) and Z = (QRS).
Consider the two statements given below:

I. Both Y and Z are in BCNF
II. Decomposition of X into Y and Z is dependency preserving and lossless.

Which of the above statements is/are correct?
 A Both I and II B I only C II only D Neither I nor II
GATE CSE 2019   Database Management System
Question 4 Explanation:
 Question 5
The set of attributes X will be fully functionally dependent on the set of attributes Y if the following conditions are satisfied.
 A X is functionally dependent on Y B X is not functionally dependent on any subset of Y C Both (A) and (B) D None of these
ISRO CSE 2018   Database Management System
Question 5 Explanation:
 Question 6
For a database relation R(a,b,c,d) where the domain of a,b,c and d include only atomic value, only the following functions dependencies and those that can be inferred from them hold
a$\rightarrow$c
b$\rightarrow$d
The relation is in:
 A First normal form but not in second normal form B Second normal form but not in third normal form C Third normal form D None of the above
ISRO CSE 2018   Database Management System
Question 6 Explanation:
 Question 7
Consider the following four relational schemas. For each schema, all non-trivial functional dependencies are listed. The underlined attributes are the respective primary keys.

Which one of the relational schemas above is in 3NF but not in BCNF?
 A Schema I B Schema II C Schema III D Schema IV
GATE CSE 2018   Database Management System
Question 7 Explanation:
 Question 8
The following functional dependencies hold true for the relational schema R{V,W,X,Y,Z}:
V $\rightarrow$W
VW $\rightarrow$X
Y$\rightarrow$ VX
Y $\rightarrow$Z
Which of the following is irreducible equivalent for this set of functional dependencies ?
 A V $\rightarrow$W V$\rightarrow$X Y $\rightarrow$V Y $\rightarrow$Z B V $\rightarrow$W W $\rightarrow$X Y$\rightarrow$ V Y$\rightarrow$ Z C V $\rightarrow$W V$\rightarrow$ X Y$\rightarrow$ V Y $\rightarrow$X Y $\rightarrow$Z D V $\rightarrow$W W$\rightarrow$ X Y$\rightarrow$ V Y $\rightarrow$X Y $\rightarrow$Z
GATE CSE 2017 SET-1   Database Management System
Question 8 Explanation:
 Question 9
A database of resear charticles in a journal uses the following schema.

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
GATE CSE 2016 SET-1   Database Management System
Question 9 Explanation:
 Question 10
Consider the relation X(P,Q,R,S,T,U) with the following set of functional dependencies
F= {{P,R}$\rightarrow${S,T}, {P,S,U}$\rightarrow${Q,R} }
Which of the following is the trivial functional dependency in $F^{+}$, where $F^{+}$ is closure of F ?
 A {P,R}$\rightarrow${S,T} B {P,R}$\rightarrow${R,T} C {P,S}$\rightarrow${S} D {P,S,U}$\rightarrow${Q}
GATE CSE 2015 SET-3   Database Management System
Question 10 Explanation:
There are 10 questions to complete.

### 7 thoughts on “Normal Form”

1. Sir, Please check question number 24. Half question is something else, and half is something else.

• Thank You Ashutosh,
We have updated the question.

• Answer is (B) only. You can check the details solution.

2. In Question Number 34, there is printing mistake in ( A→→BC )
The correct option is : i) if A→→B and A→→C then A→BC