Relational Algebra GATE CS PYQ Quiz

Consider the following relations A, B, C. How many tuples does the result of the following relational algebra expression contain? Assume that the schema of A U B is the same as that of A. 

Table A
Id   Name    Age
----------------
12   Arun    60
15   Shreya  24
99   Rohit   11

Table B
Id   Name   Age
----------------
15   Shreya  24
25   Hari    40
98   Rohit   20
99   Rohit   11

Table C
Id   Phone  Area
-----------------
10   2200   02  
99   2100   01

Suppose (

A

, B) and (

C

,D) are two relation schemas. Let r1 and r2 be the corresponding relation instances. B is a foreign key that refers to C in r2. If data in r1 and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE?

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

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?

Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation.

employee (empId, empName, empAge)
dependent(depId, eId, depName, depAge) 

Consider the following relational algebra query:

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

1) Let R and S be two relations with the following schema
R (P,Q,R1,R2,R3)
S (P,Q,S1,S2)
Where {P, Q} is the key for both schemas. Which of the following queries are equivalent?

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 ?

Given the STUDENTS relation as shown below. 

For (StudentName, StudentAge) to be the key for this instance, the value X should not be equal to

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?

Given the relations

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

Which of the following queries cannot be expressed using the basic relational algebra operations (U, -, x,[Tex]\pi[/Tex], [Tex]\sigma[/Tex], [Tex]\rho[/Tex])?