Functional Dependencies MCQ

 

Functional Dependencies

1. We can use the following three rules to find logically implied functional dependencies. This collection of rules is called

a) Axioms

b) Armstrong’s axioms

c) Armstrong

d) Closure

2. Which of the following is not Armstrong’s Axiom?

a) Reflexivity rule

b) Transitivity rule

c) Pseudotransitivity rule

d) Augmentation rule

3.  There are two functional dependencies with the same set of attributes on the left side of the arrow:

A->BC

A->B

This can be combined as

a) A->BC

b) A->B

c) B->C

d) None of the mentioned

4. Consider a relation R(A,B,C,D,E) with the following functional dependencies:

ABC -> DE and

D -> AB

The number of superkeys of R is:

a) 2

b) 7

c) 10

d) 12

5. Suppose relation R(A,B,C,D,E) has the following functional dependencies:

A -> B

B -> C

BC -> A

A -> D

E -> A

D -> E

Which of the following is not a key?

a) A

b) E

c) B, C

d) D

Let R= (A, B, C, D, E, F) be a relation scheme with the following  dependencies: C->F, E->A, EC->D, A->B.  Which of the following is a key for R?

A.) CD

B.) EC

C.) AE

D.) AC

Consider a relation scheme R = (A, B, C, D, E, H) on which the following functional dependencies hold: {A–>B, BC–>D, E–>C, D–>A}. What are the candidate keys of R?

A). AE, BE

B). AE, BE, DE

C). AEH, BEH, BCH

D). AEH, BEH, DEH

Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.

F={CH->G, A->BC, B->CFH, E->A, F- >EG} is a set of functional dependencies (FDs) so that F + is exactly the set of FDs that hold for R. How many candidate keys does the relation R have?

A.) 3

B.) 4

C.) 5

D.) 6

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?

A.) {E,F}

B.) {E,F,H}

C.) {E,F,H,K,L}

D.) {E}

If a functional dependency set F is {A→B, BC→E, ED→A, EF→G, E→F}, find the closure of attribute set (AC)

A.) {A,B,C,E,F,G}

B.) {A,B,C,D,E,F,G}

C.) {A,B,C,D,E,F}

D.) {A,B,C,D,E,G}

A relation R(ABC) is having the following 4 tuples: (1,2,3), (4,2,3), (5,3,3) and (2,4,4). Which of the following dependency can you infer doesn't hold over relation R?

A.) A→B

B.) AB→C

C.) B→C

D.) C→B