Functional Dependency & Decomposition GATE CS PYQ Quiz

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Question 1

Consider a schema R(A,B,C,D) and functional dependencies A->B and C->D. Then the decomposition of R into R1(AB) and R2(CD) is

  • dependency preserving and lossless join

  • lossless join but not dependency preserving

  • dependency preserving but not lossless join

  • not dependency preserving and not lossless join

Question 2

R(A,B,C,D) is a relation. Which of the following does not have a lossless join, dependency preserving BCNF decomposition?

  • A->B, B->CD

  • A->B, B->C, C->D

  • AB->C, C->AD

  • A ->BCD

Question 3

Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE ?

  • R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute

  • R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key

  • R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key

  • A cell in R holds a set instead of an atomic value

Question 4

Suppose the following functional dependencies hold on a relation U with attributes P,Q,R,S, and T: 

P → QR
RS → T

Which of the following functional dependencies can be inferred from the above functional dependencies?

  • PS → T

  • R → T

  • P → R

  • PS → Q

Question 5

Given the following relation instance. 

x  y  z
1  4  2
1  5  3
1  6  3
3  2  2

Which of the following functional dependencies are satisfied by the instance? (GATE CS 2000)

  • XY -> Z and Z -> Y

  • YZ -> X and Y -> Z

  • YZ -> X and X -> Z

  • XZ -> Y and Y -> X

Question 6

From the following instance of a relation scheme R (A, B, C), we can conclude that :

ABC
111
110
232
232

  • A functionally determines B and B function­ally determines C

  • A functionally determines B and B does not functionally determine C

  • B does not functionally determine C

  • A does not functionally determine B and B does not functionally determine C

Question 7

The relation scheme Student Performance (name, courseNo, rollNo, grade) has the following functional dependencies: 

name, courseNo → grade
rollNo, courseNo → grade
name → rollNo
rollNo → name

The highest normal form of this relation scheme is

  • 2 NF

  • 3 NF

  • BCNF

  • 4NF

Question 8

Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, N} and the set of functional dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N} on R. What is the key for R?

  • {E, F}

  • {E, F, H}

  • {E, F, H, K, L}

  • {E}

Question 9

Consider the relation X(P, Q, R, S, T, U) with the following set of functional dependencies 

F = {
       {P, R} → {S,T},  
       {P, S, U} → {Q, R}
    }

Which of the following is the trivial functional dependency in F+ is closure of F?

  • {P,R}→{S,T}

  • {P,R}→{R,T}

  • {P,S}→{S}

  • {P,S,U}→{Q}

Question 10

Consider the relation R(P,Q,S,T,X,Y,Z,W) with the following functional dependencies.


Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.


Which one of the following options is correct?

  • D1 is a lossless decomposition, but D2 is a lossy decomposition

  • D1 is a lossy decomposition, but D2 is a lossless decomposition

  • Both D1 and D2 are lossless decompositions

  • Both D1 and D2 are lossy decompositions

There are 17 questions to complete.

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