GATE CSEIT\/Database Relational algebra part 1 ( Selection and projection operator).<\/p>\n
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Relational algebra is a foundational aspect of database query languages, providing a formal framework for manipulating and retrieving data from relational databases. Two fundamental unary operations in relational algebra are selection<\/strong> and projection<\/strong>.<\/p>\n Selection Operator (\u03c3):<\/strong><\/p>\n The selection operator filters rows (tuples) from a relation based on a specified predicate. It retrieves only those tuples that satisfy the given condition, effectively performing a horizontal partitioning of the relation. The general form of the selection operation is:<\/p>\n \u03c3condition(R)\\sigma_{\\text{condition}}(R)<\/span>\u03c3<\/span>condition<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>R<\/span>)<\/span><\/span><\/span><\/span><\/p>\n Here, RR<\/span>R<\/span><\/span><\/span><\/span> represents the relation, and the condition is a predicate applied to each tuple. For example, to select employees with a salary greater than 50,000 from an ‘Employee’ relation:<\/p>\n \u03c3salary>50000(Employee)\\sigma_{\\text{salary} > 50000}(\\text{Employee})<\/span>\u03c3<\/span>salary<\/span>><\/span>50000<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>Employee<\/span><\/span>)<\/span><\/span><\/span><\/span><\/p>\n This operation will yield a relation containing only those employees whose salary exceeds 50,000.<\/p>\n Projection Operator (\u03c0):<\/strong><\/p>\n The projection operator extracts specific columns (attributes) from a relation, effectively performing a vertical partitioning. It removes duplicate rows in the result, ensuring that the output is a set of unique tuples. The general form of the projection operation is:<\/p>\n \u03c0attribute1,attribute2,\u2026,attributeN(R)\\pi_{\\text{attribute1}, \\text{attribute2}, \\ldots, \\text{attributeN}}(R)<\/span>\u03c0<\/span>attribute1<\/span>,<\/span>attribute2<\/span>,<\/span>\u2026<\/span>,<\/span>attributeN<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>R<\/span>)<\/span><\/span><\/span><\/span><\/p>\n For example, to retrieve only the names and departments of all employees from an ‘Employee’ relation:<\/p>\n \u03c0name,department(Employee)\\pi_{\\text{name}, \\text{department}}(\\text{Employee})<\/span>\u03c0<\/span>name<\/span>,<\/span>department<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>(<\/span>Employee<\/span><\/span>)<\/span><\/span><\/span><\/span><\/p>\n This operation will produce a relation containing unique combinations of employee names and their corresponding departments.<\/p>\n Key Differences:<\/strong><\/p>\n Example:<\/strong><\/p>\n Consider a ‘Student’ relation with attributes (StudentID, Name, Age, Major):<\/p>\n\n