The following relation records the age of 500 employees of a company, where empNo (indicating the employee number) is the key: empAge( empNo, age) Consider the following relational algebra expression: empNo(empAge (age > age1) hoempNo1, age1(empAge)) What does the above expression generate? A) Employee numbers of only those employees whose age is the maximum. B) Employee numbers of only those employees whose age is more than the age of exactly one other employee. C) Employee numbers of all employees whose age is not the minimum. D) Employee numbers of all employees whose age is the minimum.

Official answer: C) Employee numbers of all employees whose age is not the minimum.. Explanation: Let us analyze the given relational algebra expression step by step: 1. Renaming: hoempNo1, age1(empAge) creates a copy of the relation empAge with attributes renamed to (empNo1, age1). 2. Theta Join: The join condition is age > age1: empAge (age > age1) hoempNo1, age1(empAge) This condition pairs an employee from the first relation with any employee in the second relation who has a strictly smaller age. 3. Condition for inclusion: A tuple from empAge appears in this join result if and only if there exists at least one tuple in the relation whose age is strictly less than this employee's age (age > age1). - For an employee with the minimum age, there is no employee in the table with an age strictly less than theirs. Thus, their tuple fails the join condition and does not appear in the result. - For every other employee (whose age is strictly greater than at least one other employee), their tuple satisfies the condition and is included. 4. Projection: empNo( ) selects the employee numbers (empNo) of all tuples surviving the join. Therefore, the expression returns the employee numbers of all employees whose age is not the minimum, which corresponds to option (C).

A) Employee numbers of only those employees whose age is the maximum.

B) Employee numbers of only those employees whose age is more than the age of exactly one other employee.

C) Employee numbers of all employees whose age is not the minimum.

D) Employee numbers of all employees whose age is the minimum.

Databases · Relational Algebra

Official IIT answer key · IIT Bombay · Audited Aug 2026

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GATE CSE 2021 Set 1 Q27 · MCQ · 2 marks

The following relation records the age of 500 employees of a company, where $empNo$ (indicating the employee number) is the key: $empAge(\underline{empNo}, age)$ Consider the following relational algebra expression: $\Pi_{empNo}(empAge \bowtie_{(age > age1)} ho_{empNo1, age1}(empAge))$ What does the above expression generate?

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Relational Algebra

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How GATE tests Relational Algebra

Relational Algebra in GATE CS is tested through both procedural evaluation (calculating the size or contents of an output relation from given instance tables) and semantic/algebraic properties (query optimization equivalences and self-join query semantics). Questions test core operators such as selection ( ), projection ( ), set union ( ), renaming ( ), and theta/equi-joins ( ). Questions alternate between 1-mark mechanical/equivalence checks and 2-mark semantic interpretation or multi-step tuple evaluations.

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Databases · Relational Algebra

Official IIT answer key · IIT Bombay · Audited Aug 2026

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GATE CSE 2021 Set 1 Q27 · MCQ · 2 marks

The following relation records the age of 500 employees of a company, where $empNo$ (indicating the employee number) is the key: $empAge(\underline{empNo}, age)$ Consider the following relational algebra expression: $\Pi_{empNo}(empAge \bowtie_{(age > age1)} ho_{empNo1, age1}(empAge))$ What does the above expression generate?

Select an option to check

Key concept

Relational Algebra

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Relational Algebra

Full Relational Algebra guide →

More on Relational Algebra

All 4 questions on Relational Algebra →

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

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