What is the optimized version of the relation algebra expression A1( A2( F1( F2(r)))), where A1, A2 are sets of attributes in r with A1 A2 and F1, F2 are Boolean expressions based on the attributes in r? A) A1( (F1 F2)(r)) B) A1( (F1 F2)(r)) C) A2( (F1 F2)(r)) D) A2( (F1 F2)(r))

Official answer: A) A1( (F1 F2)(r)). Explanation: We use standard relational algebra equivalence rules: 1. Cascade of Selections: F1( F2(r)) F1 F2(r) Applying consecutive selection conditions is equivalent to applying a single selection with the logical AND of the conditions. 2. Cascade of Projections: If A1 A2, then: A1( A2(E)) A1(E) Because A1 is a subset of A2, projecting onto A2 first and then onto A1 preserves the exact same set of attributes as directly projecting onto A1. Combining these two optimizations gives: A1( (F1 F2)(r)) Thus, option (A) is the correct optimized expression.

Databases · Relational Algebra

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 3 Q21 · MCQ · 1 mark

What is the optimized version of the relation algebra expression $\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$ , where $A1, A2$ are sets of attributes in $r$ with $A1 \subset A2$ and $F1, F2$ are Boolean expressions based on the attributes in $r$ ?

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

Databases · Relational Algebra

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 3 Q21 · MCQ · 1 mark

What is the optimized version of the relation algebra expression $\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$ , where $A1, A2$ are sets of attributes in $r$ with $A1 \subset A2$ and $F1, F2$ are Boolean expressions based on the attributes in $r$ ?

Select an option to check

Key concept

Relational Algebra

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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.

What is the optimized version of the relation algebra expression $\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$ , where $A1, A2$ are sets of attributes in $r$ with $A1 \subset A2$ and $F1, F2$ are Boolean expressions based on the attributes in $r$ ?

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What is the optimized version of the relation algebra expression $\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$ , where $A1, A2$ are sets of attributes in $r$ with $A1 \subset A2$ and $F1, F2$ are Boolean expressions based on the attributes in $r$ ?

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