Relational Algebra and SQL Queries Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Relational Algebra and SQL Queries notes for GATE DA: 53 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    Chapter Roadmap: Relational Algebra and SQL Queries

    Your Learning Journey
    1

    Relational Algebra & Semantics

    Formal query language using mathematical operations. Highest weightage topic.

    2

    SQL Joins, Aggregation & Grouping

    Practical SQL implementation with table combinations and summary computations.

    3

    SQL Subqueries & Evaluation

    Nested queries and execution semantics. Understand internal processing.

    By the end of this chapter, you will:
    • Write queries in both relational algebra and SQL
    • Predict query results for any given database instance
    • Understand join semantics and aggregation behavior
    • Analyze nested queries and their execution order

    What is Relational Algebra?

    The Core Idea

    Relational algebra is a procedural query language that operates on relations (tables) to produce new relations.

    InputOne or two relations
    OutputA new relation (table)
    ProceduralSpecifies how to get the result
    ComposableOutput becomes next input

    The Six Fundamental Operations

    OperationSymbolPurpose
    SelectFilter rows
    ProjectFilter columns
    UnionCombine rows
    DifferenceRemove rows
    ProductAll combinations
    RenameRename attrs

    Select Operation: Filtering Rows

    Select (): Row Filter

    • R = input relation
    • condition = predicate using attributes of R
    • Output = subset of rows satisfying condition
    • Schema (columns) remains unchanged

    Example

    Relation: Employee(EmpID, Name, Salary, Dept)

    SELECT * FROM Employee WHERE Salary > 50000 AND Dept = 'IT';
    Select does not change the schema. It only reduces the number of tuples (rows).

    Project Operation: Filtering Columns

    Project (): Column Selector

    • Output has only specified columns
    • Duplicates are automatically removed (relation is a set)
    Critical Point: Since a relation is a set, project removes duplicate tuples. This is different from SQL's SELECT without DISTINCT.

    Example

    Before ProjectAfter
    (Alice, IT, 60k)(Alice, IT)
    (Bob, HR, 55k)(Bob, HR)
    (Alice, IT, 70k)(Alice, IT)

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    Relational Algebra and SQL Queries Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

    Relational Algebra and SQL Queries notes for GATE DA: 53 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

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