set intersection in relational algebra in dbms

Set intersection in relational algebra, examples for set intersection, equivalent relational algebra expression for intersection operator, equivalent SQL queries for relational algebra intersection operator

Set Intersection

Operation	INTERSECTION
Type of operation	Binary
Syntax	R1 ∩ R2      Example: DEPOSITOR ∩ BORROWER (Expression1) ∩ (Expression2)      Example: Π regno (student) ∩ Π regno (sub_regd)
Rules to be satisfied	To perform difference operation, the following conditions must hold; 1. Both the relations R1 and R2 (or the result of expression 1 and expression 2) must have the same number of attributes. That is, Arity should be same. 2. The domain of ith attribute of R1 and ith attribute of R2 must be same for all i.
Function	INTERSECTION operation finds the records that are in both relations. If we find intersection between relations R1 and R2, then the records that are in both R1 and R2 become part of new result relation.
Purpose	To perform set operation. For example, assume that you have two relations as depositor and borrower. If we would like to find the customers who are both depositors and borrowers from the bank, we can perform intersection between these two tables.
Example 1	The table STU_INDOOR records information about the indoor sports entry of students. The table STU_OUTDOOR stores information about the outdoor sports entry of students. STU_INDOOR Regno Sport 3 records BIT001 Chess BIT023 Carrom BCE020 Badminton STU_OUTDOOR Regno Sport 3 records BIT001 Soccer BIT023 Soccer BME023 Cricket Find the regno of students who plays both indoor and outdoor sports. RA: (Π regno (stu_indoor)) ∩ (Π regno (stu_outdoor)) SQL: (SELECT regno FROM stu_indoor) INTERSECT (SELECT regno FROM stu_outdoor); Result: Finds the tuples that are in both stu_indoor and stu_outdoor relations; (Π regno (stu_indoor)) ∩ (Π regno (stu_outdoor)) Regno BIT001 BIT023
Example 2	Consider the tables below; STU_INDOOR Regno Sport 4 records BIT001 Chess BIT023 Carrom BCE020 Badminton BEE001 Badminton STU_OUTDOOR Regno Sport 3 records BIT001 Soccer BIT023 Soccer BCE020 Cricket Find the regno of students who plays both badminton and any of the outdoor sports. RA: (Π regno (σsport = ‘Badminton’(stu_indoor))) ∩ (Π regno (stu_outdoor)) SQL: (SELECT regno FROM stu_indoor WHERE sport=’Badminton’) INTERSECT (SELECT regno FROM stu_outdoor); Result: Finds the tuples that are in both in stu_indoor and stu_outdoor relations but plays only badminton as indoor sport; (Π regno (σsport = ‘Badminton’ (stu_indoor))) Regno BCE020 BEE001  Final result (Π regno (σsport = ‘Badminton’ (stu_indoor))) ∩ (Π regno (stu_indoor)) Regno BCE020

Note:

Intersection can be expressed using set difference operator as follows;

R1 ∩ R2 = R1 – (R1 – R2)

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