ER and Relational Models

Question 21

Consider the join of a relation R with a relation S. If K has m tuples and S has n tuples, then the maximum and minimum sizes of the join respectively are:

• m+n and 0
• mn and 0
• m+n and m-n
• mn and m+n

Question 22

The relational algebra expression equivalent to the following tuple calculus expression

{ t | t ∈ r ∧ (t[A] = 10 ∧ t[B] = 20 }

is

• a
• b
• c
• d

Question 23

Given two union compatible relations R₁(A,B) and R₂(C,D). What is the result of the operation R₁⋈_{A=C∧ B=D} R₂    A. R₁ ∪ R₂ B. R₁ Χ R₂ C. R₁ - R₂ D. R₁ ∩ R₂

• a
• b
• c
• d

Question 24

Which of the following query transformations (i.e., replacing the l.h.s. expression by the r.h.s. expression) is incorrect? R₁ and R₂ are relations. C₁, C₂ are selection conditions and A₁, A₂ are attributes of R₁. a.  σC₁( σC₂R1)) → σC₂(σC₁(R1)) b.  σC₁( π_A1R1)) → π_A1(σC₁(R1)) c.  σC₁( R₁ ∪ R₂ ) → σC₁(R₁) ∪ σC₁(R₂) d.  π_A1(σC₁(R₁)) → σC₁ (πA₁ (R₁))

• a
• b
• c
• d

Question 25

A library relational database system uses the following schema

USERS (User#, UserName, HomeTown)
BOOKS (Book#, BookTitle, AuthorName)
ISSUED (Book#, User#, Date)

Explain in one English sentence, what each of the following relational algebra queries is designed to determine  

[caption width="800"] [/caption]

•  Show all the Book Title which have been issued by User# 6.

•  The user who’s home town is Delhi and issued a book, Show all the name authors of the book he/she have issued.

Question 26

Consider the following tables T1 and T2: In table T1, P is the primary key, Q is the foreign key referencing R in table T2 with on-delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in the table T1 with on-delete set NULL and on-update cascade. In order to delete record (3,8) from table, numbers of additional record that need to be deleted from table T1 is ______. Note: This question appeared as Numerical Answer Type.

• 0
• 1
• 2
• 3

Question 27

In an Entity-Relationship (ER) model, suppose R is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in R and that the cardinality of E1 is greater that the cardinality of E2. Which one of the following is true about R?

• Every entity in E1 is associated with exactly one entity in E2.
• Some entity in E1 is associated with more than one entity in E2.
• Every entity in E2 is associated with exactly one entity in E1.
• Every entity in E2 is associated with at most one entity in E1.

Question 28

Consider the relations r(A, B) and s(B, C), where s.B is a primary key and r.B is a foreign key referencing s.B. Consider the query Q: r⋈(σ_B<5(s)) Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values. Which one of the following is NOT equivalent to Q?

• σ_B<5(r ⋈ s)
• σ_B<5(r LOJ s)
• r LOJ (σ_B<5(s))
• σ_B<5(r)LOJ s

Question 29

Match the following with respect to RDBMS :

• (1)
• (2)
• (3)
• (4)

Question 30

Consider the following schema :

Sailors (sid, sname, rating, age)
Boats (bid, bname, colour)
Reserves (sid, bid, day)

Two boats can have the same name but the colour differentiates them. The two relations

ρ (Tempsids, (Ⲡ  sid, bid  Reserves)/(Ⲡ bid ( σ bname =\'Ganga\' Boats))),
Ⲡ sname (Tempsids ⋈ Sailors)

If / is division operation, the above set of relations represents the query

• Names of sailors who have reserved all boats called Ganga
• Names of sailors who have not reserved any Gangaboat
• Names of sailors who have reserved at least one Gangaboat
• Names of sailors who have reserved at most one Ganga boat