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Relational Algebra in DBMS
Question 1
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?
(GATE 2012 | MCQ | 1-Mark)
[Tex]\Pi_B(r_1) - \Pi_C(r_2) = \emptyset[/Tex]
[Tex]\Pi_C(r_2) - \Pi_B(r_1) = \emptyset[/Tex]
[Tex]\Pi_B(r_1) = \Pi_C(r_2)[/Tex]
[Tex]\Pi_B(r_1) - \Pi_C(r_2)[/Tex] ≠ [Tex]\emptyset[/Tex]
Question 2
What is the result of ∏ADDRESS(STUDENT) where STUDENT has duplicate 'DELHI' addresses?
Returns all addresses including duplicates
Returns only unique addresses
Returns an error due to duplicate elimination
Returns NULL values for duplicates
Question 3
Consider the relations R(A, B) and (B, C). Let the result of the following relational algebra expression be relation T:
[Tex]T = (\Pi_{A}(R)) - (\Pi_{A}(R \bowtie S))[/Tex]
Which of the following statements correctly describes the contents of relation T?
(GATE 2022 | MCQ | 2-Mark)
T contains values of A that are present in R and have at least one matching tuple in S
T contains values of A that are present in R and do not have any matching tuple in S
T contains values of A that are present in both R and S
T is always empty
Question 4
Which of the following operations on two relations R and S cannot be implemented using only the basic relational algebra operators (Selection [Tex]\sigma[/Tex], Projection [Tex]\pi[/Tex], Cartesian Product $\times$, Union [Tex]\cup[/Tex], and Set Difference -)?
(GATE 2021 | MCQ | 1-Mark)
Left Outer Join [Tex](\bowtie_{L})[/Tex]
Division [Tex](\div)[/Tex]
Intersection [Tex](\cap)[/Tex]
None
Question 5
Which of the following relational algebra expressions is/are not logically equivalent to the relational intersection operation [Tex]R \cap S[/Tex], assuming R and S are two union-compatible relations?
(GATE 2021 | MCQ | 1-Mark)
R - (R - S)
S - (S - R)
[Tex](R \cup S) - ((R - S) \cup (S - R))[/Tex]
[Tex](R - S) \cup (S - R)[/Tex]
Question 6
The Relational Division operator ([Tex]\div[/Tex]) is a specialized extended operator. If relation R has attributes (X, Y) and relation S has attribute (Y), which of the following processes or components is/are NOT a valid intermediate step when evaluating the division expression [Tex]\pi_X(R)[/Tex] - [Tex]\pi_X((\pi_X(R) \times S) - R)[/Tex]?
(GATE 2021 | MCQ | 1-Mark)
Finding all theoretically possible pairings of X values from R with all Y values from S via a Cartesian Product.
Filtering out pairs that actually exist in the original relation R using Set Difference
Finding the intersection of attributes between R and S using a Natural Join condition
Projecting the disqualified X values to subtract them from the absolute pool of all X values
Question 7
Which operation implements "students who don't play any sports"?
STUDENT - STUDENT_SPORTS
∏ROLL_NO(STUDENT) - ∏ROLL_NO(STUDENT_SPORTS)
σ(ROLL_NO=NULL)(STUDENT ⋈ STUDENT_SPORTS)
STUDENT ÷ STUDENT_SPORTS
Question 8
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.
[Tex](A \cup B) \bowtie_{A.Id > 40 \vee C.Id < 15} C[/Tex]
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
(GATE 2012 | MCQ | 2-Mark)
7
4
5
9
Question 9
Which relational algebra expression is equivalent to SQL's LEFT JOIN?
R ⋈ S
R ⟕ S
(R × S) ∪ (R × (∏(NULL,...,NULL)(S)))
(R ⋈ S) ∪ (R - ∏R.*(R ⋈ S))
Question 10
What distinguishes θ-join from equijoin?
θ-join uses only = operator
Equijoin eliminates duplicate columns
θ-join supports inequality conditions
Equijoin requires natural join
There are 10 questions to complete.