GATE CS 2017 Set 1 — Question 41

MCQ+2 / -0.67MediumTuple Relational CalculusRelational ModelDatabases

Databases → Relational Model → Tuple Relational Calculus

Last updated 5 September 2026

Question

\{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}]))\}

Correct answer (D) (I), (II) and (III) Solution A query in Tuple Relational Calculus (TRC) is safe if it produces a finite number of tuples. In the context of database theory questions (like in GATE), safety is often evaluated under the Active Domain Assumption, meaning the domain of attributes is restricted to the finite set of values currently present in the database instance. Query (I): Selects tuples where DeptId is not equal to any DeptId in DEPT. Under the active domain assumption, the set of values in the domain but not in DEPT is finite. Thus, it is safe. Query (II): Selects tuples where DeptId is not equal to some DeptId in DEPT. This is also finite under the active domain assumption. Query (III): Selects tuples where DeptId is equal to some DeptId in DEPT. This restricts DeptId to values in the relation, so it is definitely finite and safe. Therefore, all three queries are considered safe in this context. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (D) (I), (II) and (III) Solution A query in Tuple Relational Calculus (TRC) is safe if it produces a finite number of tuples. In the context of database theory questions (like in GATE), safety is often evaluated under the Active Domain Assumption, meaning the domain of attributes is restricted to the finite set of values currently present in the database instance. Query (I): Selects tuples where DeptId is not equal to any DeptId in DEPT. Under the active domain assumption, the set of values in the domain but not in DEPT is finite. Thus, it is safe. Query (II): Selects tuples where DeptId is not equal to some DeptId in DEPT. This is also finite under the active domain assumption. Query (III): Selects tuples where DeptId is equal to some DeptId in DEPT. This restricts DeptId to values in the relation, so it is definitely finite and safe. Therefore, all three queries are considered safe in this context.

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