Relational Algebra · Database Management System · GATE CSE

Consider the following two relations, R(A, B) and S(A, C):

The total number of tuples obtained by evaluating the following expression

$$ \sigma_{B < C}(R \bowtie_{R.A = S.A} S) $$

is _________

Consider the following three relations in a relational database.

Employee ( $$\underline {eld} $$ , Name), Brand ( $$\underline {bld} $$ , bName), Own ( $$\underline {eld} $$ , $$\underline {bld} $$)

Which of the following relational algebra expressions return the set of elds who own all the brands?

A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of σ_{(A>10)∨(B=18)}(r) is ______

Which of the following tuple relational calculus expression(s) is/are equivalent to $$\forall t \in r \left(P\left(t\right)\right)$$?

I) Relational algebra
II) Tuple relational calculus restricted to safe expressions
III) Domain relational calculus restricted to safe expressions

Let r be a relation instance with schema R = (A, B, C, D).

Select distinct a1, a2, ..., an 

From r1, r2, ..., rm 

Where P; 

Given the relations

employee (name, salary, deptno), and
department (deptno, deptname, address)

The relational algebra expression equivalent to the following tuple calculus expression:

The relation schema, Person($\underline{\text{pid}}$, $city$), describes the city of residence for every person uniquely identified by $pid$. The following relational algebra operators are available: selection, projection, cross product, and rename.

To find the list of cities where at least 3 persons reside, using the above operators, the minimum number of cross product operations that must be used is

$$Q:$$ $$\,\,\,\,\,\,\,\,\,$$ $$r$$ $$\,\,\,\,$$ $$\bowtie$$ $$\,\,\,\,$$ $$\left( {{\sigma _{b < 5}}\left( s \right)} \right)$$

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 $$Q$$?

employee (empId, empName, empAge)

dependent (depId, eId, depName, depAge)

The above query evaluates to the set of empIds of employees whose age is greater than that of

How many tuples does the result of the following SQL query contain?

SELECT A.Id 
FROM A 
WHERE A.Age > ALL (SELECT B.Age 
                   FROM B 
                   WHERE B.Name = 'Arun')

How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A ∪ B is the same as that of A. $$(A\cup B)\bowtie _{A.Id > 40 \vee C.Id < 15} C$$

$$Q1: \pi_{A_1, \dots ,A_p} \left(\sigma_{A_p=c}\left(r\right)\right)$$ where is a constant

$$Q2: \pi_{A_1, \dots ,A_p} \left(\sigma_{c_1 \leq A_p \leq c_2}\left(r\right)\right)$$ where c₁ and c₂ are constants

The database can be configured to do ordered indexing on A_p or hashing on A_p. Which of the following statements is TRUE?

The relation R contains 200 tuples and the relation S contains 100 tuples. What is the maximum number of tuples possible in the natural join R $$\Join$$ S?

R (P, Q, R1, R2, R3)

S (P, Q, S1, S2)

b-Schema = (b-name, b-city, assets)
a-Schema = (a-num, b-name, bal)
d-Schema = (c-name, a-number)

Let branch, account and depositor be respectively instances of the above schemas. Assume that account and depositor relations are much bigger than the branch relation.

Which one of the following queries is the most efficient version of the above query ?

Consider the relation employee(name, sex, supervisorName) with name as the key, supervisorName gives the name of the supervisor of the employee under consideration. What does the following Tuple Relational Calculus query produce?

Information about a collection of students is given by the relation studInfo(studId, name, sex). The relation enroll(studId, courseId) gives which student has enrolled for (or taken) what course(s). Assume that every course is taken by at least one male and at least one female student. What does the following relational algebra expression represent?

Table: student

Table: hobby

The following SQL query is executed on the above tables:

Select hostel
From student natural join hobby
Where marks > = 75 and roll between 2000 and 3000;

Relations S and H with the same schema as those of these two tables respectively contain the same information as tuples. A new relation S’ is obtained by the following relational algebra operation:

The difference between the number of rows output by the SQL statement and the number of tuples in S’ is

A library relational database system uses the following schema

USERS (User #, User Name, Home Town)

BOOKS (Books # Book Title, Author Name)

ISSUED (Book #, User #, Date)

(a) $$\sigma_{ \text{User#}=6}\left(\pi_{\text{User#, Book Title}}\left(\left(\text{USERS} \bowtie \text{ISSUED}\right) \bowtie \text{BOOKS}\right)\right)$$