GATE CSE 2001 | Relational Algebra Question 28 | Database Management System

GATE CSE 2001

MCQ (Single Correct Answer)

-0.6

Which of the following relational calculus expressions is not safe?

$$\left\{t \mid \exists u \in R_1\left(t[A] = u[A]\right) \land \neg \exists s \in R_2 \left(t[A] = s[A]\right)\right\}$$

$$\left\{ t \mid \forall u \in R_1\left(u[A]="x"\Rightarrow \exists s \in R_2\left(t[A] = s[A] \land s[A] = u[A]\right)\right) \right\}$$

$$\left\{t \mid \neg (t \in R_1)\right\}$$

$$\left\{t \mid \exists u \in R_1\left(t[A]=u[A]\right) \land \exists s \in R_2 \left(t[A] = s[A]\right)\right\}$$

GATE CSE 1998

MCQ (Single Correct Answer)

-0.6

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?

$$\sigma_{C_1} \left(\sigma_{C_2}\left(R_1\right)\right) \to \sigma_{C_2} \left(\sigma_{C_1}\left(R_1\right)\right)$$

$$\sigma_{C_1} \left(\pi_{A_1}\left(R_1\right)\right) \to \pi_{A_1} \left(\sigma_{C_1}\left(R_1\right)\right)$$

$$\sigma_{C_1} \left(R_1 \cup R_2\right) \to \sigma_{C_1}\left(R_1\right) \cup \sigma_{C_1} \left(R_2\right)$$

$$\pi_{A_1} \left(\sigma_{C_1}\left(R_1\right)\right) \to \sigma_{C_1} \left(\pi_{A_1}\left(R_1\right)\right)$$

GATE CSE 1996

Subjective

-0

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)

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

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

(b) $$\pi_{\text{Author Name}}\left(\text{BOOKS} \bowtie \sigma_{\text{Home Town=Delhi}} \left(\text{USERS} \bowtie \text{ISSUED}\right)\right)$$