Relational Algebra


Question 1
Consider the following three relations in a relational database.
Employee(eId, Name), Brand (bId, bName), Own(eId ,bId)
Which of the following relational algebra expressions return the set of eIds who own all the brands?
MSQ
A
\Pi _{eId}(\Pi _{eId,bId}(Own)/\Pi _{bId}(Brand))
B
\Pi _{eId}(Own)-\Pi _{eId}\left ((\Pi _{eId}(Own) \times \Pi _{bId}(Brand) )-\Pi _{eId,bId}(Own) \right )
C
\Pi _{eId}(\Pi _{eId,bId}(Own)/\Pi _{bId}(Own))
D
\Pi _{eId}\left ((\Pi _{eId}(Own) \times \Pi _{bId}(Own) )/\Pi _{bId}(Brand) \right )
GATE CSE 2022   Database Management System
Question 2
The following relation records the age of 500 employees of a company, where empNo ( indicating the employee number) is the key:

empAge(\underline{empNo},age)

Consider the following relational algebra expression:

\Pi_{empNo}(empAge \Join_{(age > age1)} \rho_{empNo1,age1}(empAge))

What does the above expression generate?
A
Employee numbers of only those employees whose age is the maximum
B
Employee numbers of only those employees whose age is more than the age of exactly one other employee
C
Employee numbers of all employees whose age is not the minimum
D
Employee numbers of all employees whose age is the minimum
GATE CSE 2021 SET-1   Database Management System


Question 3
Consider the following relation P(X, Y, Z), Q(X, Y, T) and R(Y, V):

How many tuples will be returned by the following relational algebra query?

Answer:______
A
1
B
2
C
3
D
4
GATE CSE 2019   Database Management System
Question 4
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 \Join (\sigma _{B\lt 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 queries is NOT equivalent to Q?
A
\sigma _{B \lt 5}(r\Join s)
B
\sigma _{B\lt 5}(r LOJ s)
C
r LOJ(\sigma _{B\lt 5}(s))
D
\sigma _{B\lt 5}(r) LOJ s
GATE CSE 2018   Database Management System
Question 5
Consider a database that has the relation schema CR (StudentName, CourseName). An instance of the schema CR is as given below.

The following query is made on the database

T1\leftarrow \pi _{CourseName}(\sigma _{StudentName='SA'}(CR))
T2\leftarrow CR\div T1

The number of rows in T2 is ____________.
A
2
B
3
C
4
D
5
GATE CSE 2017 SET-1   Database Management System


There are 5 questions to complete.

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