Relational algebra is a procedural query language that uses operations on relations to produce new relations. Key operations include selection, projection, union, set difference, cartesian product, natural join, and outer join, each with specific syntax and SQL equivalents. These operations allow for various ways to manipulate and query relational data effectively.

1. Topic: Relational Algebra
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2. What is Relational Algebra?
• Relational Algebra is a procedural query language. It
consists of a set of operations that take one or two
relations as input and produce a new relation as their
output.
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3. Fundamental Operation in Relational Algebra
• Selection
• Projection
• Union
• Set Difference
• Cartesian Product
• Natural Join
• Outer join
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4. Selection
• Selects tuples or rows that satisfy a given predicate.
• Denoted by lowercase Greek letter sigma(σ).
• Syntax: σAttribute_name=Condition/predicate(Relation/Table_name)
• SQL- SELECT * FROM `cricket` WHERE sname="A“
cricket cricket
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Output

5. Projection
• Projection operation is used to select or see any column
• Denoted by uppercase Greek letter Pi(π)
• Syntax: πAttributes_name(σAttribute_name=Condition/predicate(Relation/Table_name))
Such as πsid,sname(σscore=score>40(cricket))
• SQL- SELECT sid,sname from `cricket` WHERE score>40
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Output

6. Union
• Performed as binary union operation between two given relation or table.
This operation must satisfy two conditions. Those are
• Each table must have same numbers of attributes or columns.
• And the have same data type.
• Denoted by uppercase Greek letter Pi(π)
• Syntax: πAttributes_name (cricket) ∪πAttributes_name (football)
Such as πsid,sname(cricket) ∪ πsid,sname(football)
• SQL- SELECT sid,sname FROM cricket UNION SELECT sid,sname FROM
football;
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7. Union(Continue)
Example:
Cricket football
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Output

8. Set Difference
• Allows us to compare two tables or find records that are in one table not in
other
• Denoted by Minus(-)
• Syntax: πAttributes_name (cricket) -πAttributes_name (football)
Such as πsid,sname(cricket) - πsid,sname(football)
• SQL- Select sid,sname from cricket MINUS Select sid,sname football;
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9. Cartesian Product
• Allows us to combine information from any two relation
• Denoted by a cross(×).
• Syntax: cricket × football
• SQL-SELECT cricket.sid, cricket.sname, football.sid, football.sname
FROM cricket, football
Or, SELECT cricket.sid, cricket.sname, football.sid, football.sname
FROM cricket cross join football
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10. Cartesian Product(continue)
Example:
cricket football
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Output

11. Natural Join
• Allow us to combine certain selections and a Cartesian product into
one operation.
• Must be a common attribute between two table.
• Denoted by (⋈)
• Syntax:πAttributes_name(σCommon_column_name=Common_column_name (table1×table2)
• SQL-SELECT * FROM cricket natural join football;
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12. Natural Join(continue)
• Example:
cricket football
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Output

13. Outer Join
• Extension of Natural join.
• Deals with missing data in Natural Join.
• Normally 3 types
• Left outer Join( )
• Right outer join(⟖)
• Full outer join(⟗)
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14. Left outer join
• Returns all values of left table
• SQL-SELECT*FROM cricket LEFT JOIN football ON cricket.sid =
football.sid;
• Example:
cricket football
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15. Right outer join
• Returns all values of right table
• SQL-SELECT*FROM cricket RIGHT JOIN football ON cricket.sid =
football.sid;
• Example:
cricket football
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16. Full outer join
• Returns all values of both table. If no match found it returns NULL
• SQL-SELECT*FROM cricket FULL OUTER JOIN football ON cricket.sid =
football.sid;
• Example:
cricket football
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