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Explain Relational algebra operations

Explain following Relational algebra operations with examples.

(i) Set difference (ii) Generalized Projection

(iii) Natural join (iv) Rename

*Mumbai University > Computer Engineering > Sem 4 > Database Management System *

Marks: 10 |M

Year: May 2015

1 Answer
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  • Set Difference

    Returns all rows that are in the result of query 1 but not in the result of query.

    The relations R and S must be union-compatible, and the schema of the result is defined to be identical to the schema of R.

    • Syntax: (Query Expression 1) - (Query Expression 2).
    • Notation : R − S Finds all the tuples that are present in R but not in S. Пauthor (Books) - Пauthor (Articles)
    • Output: Provides the name of authors who have written books but not articles.
  • Generalized Projection

    • It extends the projection operation by allowing arithmetic functions to be used in projection list.
    • Syntax: П F1,F2 … Fn (E)

      Where E: relational algebra expression

      $\hspace{1cm}$Fi: arithmetic expression.

    • Example:

      Consider the Table "Credit-info" :

Customer-name Limit Credit_Balance
abc 2000 500
xyz 500 250
pqr 700 100
mno 1500 1000

i. Find how much money a person can spend.

$Π_{Customer-name,(Limit-Credit_balance)}(Credit-info)$

iii. Natural Join A natural join returns all rows by matching values in common columns having same name and data type of columns and that column should be present in both tables.

  • Example Find all employees and their department name.

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In above example both tables having ‘did’ as common column so this column is called joining column based on matching of this column, tables are joined.

iv. Rename

  • We are joining a table with itself in the relational algebra expression: it’s like joining two tables with the same name and the same attributes names. Therefore, some renaming is required in such queries.
  • We can give alternative name to any column (attribute) or any table of query expressions using operator called as RENAME operator.
  • Syntax:
    • <new_name> (<input-table_name>).
  • E: relational algebra expression
    • ρ x (E): returns the result of expression E under the name x.
    • ρ x (A1, A2, A3… An) (E): returns the result of expression E under the name x with attributes renamed to A1, A2, A3… An.
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