Database Design(Normal Forms)

Question 11

Let r be a relation instance with schema R = (A, B, C, D). We define r₁ = Π_{A, B, C} (r) and r₂ = Π_A.D (r). Let s = r₁ * r₂ where * denotes natural join. Given that the decomposition of r into r₁ and r₂ is lossy, which one of the following is TRUE?

• s ⊂ r
• r ∪ s
• r ⊂ s
• r * s = s

Question 12

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?

• AE, BE
  

• AE, BE, DE
  

• AEH, BEH, BCH
  

• AEH, BEH, DEH
  

Question 13

Let R1 (A, B, C) and R2 (D, E) be two relation schema, where the primary keys are shown underlined, and let C be a foreign key in R1 referring to R2. Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r1 and r2. Which one of the following relational algebra expressions would necessarily produce an empty relation ?

• 1
• 2
• 3
• 4

Question 14

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 15

Consider the relation Student (name, sex, marks), where the primary key is shown underlined, pertaining to students in a class that has at least one boy and one girl. What does the following relational algebra expression produce? (Note: r is the rename operator). The condition in join is "(sex = female ^ x = male ^ marks ≤ m)"

• names of girl students with the highest marks
• names of girl students with more marks than some boy student
• names of girl students with marks not less than some boy students4)
• names of girl students with more marks than all the boy students

Question 16

Consider the following functional dependencies in a database:

  Data_of_Birth → Age
  Age → Eligibility
  Name → Roll_number
  Roll_number → Name
  Course_number → Course_name
  Course_number → Instructor
  (Roll_number, Course_number) → Grade

The relation (Roll_number, Name, Date_of_birth, Age) is:

• In second normal form but not in third normal form
• In third normal form but not in BCNF
• In BCNF
• None of the above

Question 17

Relation R with an associated set of functional dependencies, F is decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set relations is.

• Zero
• More than zero but less than that of an equivalent 3NF decomposition
• Proportional to the size of F+
• Indeterminate

Question 18

With regard to the expressive power of the formal relational query languages, which of the following statements is true?

• Relational algebra is more powerful than relational calculus
• Relational algebra has the same power as relational calculus
• Relational algebra has the same power as safe relational calculus
• None of the above

Question 19

Relation R is decomposed using a set of functional dependencies, F and relation S is decomposed using another set of functional dependencies G. One decomposition is definitely BCNF, the other is definitely 3NF, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available).

• Dependency-preservation
• Lossless-join
• BCNF definition
• 3NF definition

Question 20

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

A	B	C
1	1	1
1	1	0
2	3	2
2	3	2

• 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