Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus. (I) { t ∃ u ∈ EMP(t[EmpName] = u[EmpName] ∀ v ∈ DEPT(t[DeptId] ≠ v[DeptId])) } (II) { t ∃ u ∈ EMP(t[EmpName] = u[EmpName] ∃ v ∈ DEPT(t[DeptId] ≠ v[DeptId])) } (III) { t ∃ u ∈ EMP(t[EmpName] = u[EmpName] ∃ v ∈ DEPT(t[DeptId] = v[DeptId])) } Which of the above queries are safe? A) (I) and (II) only B) (I) and (III) only C) (II) and (III) only D) (I), (II) and (III)

Official answer: D) (I), (II) and (III). Explanation: A Tuple Relational Calculus (TRC) expression { t P(t) } is said to be safe if it is guaranteed to yield a finite number of tuples whose attribute values are drawn strictly from the domain of the expression (the constants appearing in the query and the values present in the database relations). In all three expressions: - The components of the resulting tuple t are bounded by the database relations: t[EmpName] is drawn from the domain of EMP via ∃ u ∈ EMP(t[EmpName] = u[EmpName]), and t[DeptId] is constrained relative to the finite values in the DEPT / EMP relation domains. - None of the queries generate an infinite relation or depend on values from an infinite universal domain outside the database. Consequently, all three queries (I), (II), and (III) are safe. Thus, the correct option is (D).

Relational Model and SQL

GATE CSE 2017 Set 1 · Q41

MCQ2 marksHard

Time00:00

Consider a database that has the relation schemas EMP(EmpId, EmpName, DeptId), and DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus. (I) $\{ t \mid \exists u \in \text{EMP}(t[\text{EmpName}] = u[\text{EmpName}] \wedge \forall v \in \text{DEPT}(t[\text{DeptId}] \neq v[\text{DeptId}])) \}$ (II) $\{ t \mid \exists u \in \text{EMP}(t[\text{EmpName}] = u[\text{EmpName}] \wedge \exists v \in \text{DEPT}(t[\text{DeptId}] \neq v[\text{DeptId}])) \}$ (III) $\{ t \mid \exists u \in \text{EMP}(t[\text{EmpName}] = u[\text{EmpName}] \wedge \exists v \in \text{DEPT}(t[\text{DeptId}] = v[\text{DeptId}])) \}$ Which of the above queries are safe?

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Solution

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Official answer: D) (I), (II) and (III)

Relational Model and SQL

A Tuple Relational Calculus (TRC) expression $\{ t \mid P(t) \}$ is said to be safe if it is guaranteed to yield a finite number of tuples whose attribute values are drawn strictly from the domain of the expression (the constants appearing in the query and the values present in the database relations).

In all three expressions:

The components of the resulting tuple $t$ are bounded by the database relations: $t[\text{EmpName}]$ is drawn from the domain of $\text{EMP}$ via $\exists u \in \text{EMP}(t[\text{EmpName}] = u[\text{EmpName}])$ , and $t[\text{DeptId}]$ is constrained relative to the finite values in the $\text{DEPT}$ / $\text{EMP}$ relation domains.
None of the queries generate an infinite relation or depend on values from an infinite universal domain outside the database.

Consequently, all three queries (I), (II), and (III) are safe.

Thus, the correct option is (D).

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This Relational Model and SQL previous year question is Q41 of the GATE CSE 2017 Set 1 paper. Find more GATE CSE PYQs on Relational Model and SQL in Databases, or browse all GATE CSE PYQs.

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Relational Model and SQL in GATE CSE

Relational Model and SQL has 15 GATE CSE PYQs across 12 papers from 2011 to 2026. 8 of them are 2-mark MCQs like this one, and GATE CSE 2017 Set 1 has 3.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.