DBMS Notes

Binary Operators in Relational Algebra

All those Operators which operate on two operands are known as Binary operators.

Types of Binary Operators

There are 3 types of binary operators which are given below

  1. Union Operators
  2. Cross Product
  3. Difference operator

1. Union Operator (∪)

Let A and B be two relations.

Then

  • A ∪ B is the set of all tuples belonging to either A or B or both.
  • In A ∪ B, duplicates are automatically removed.
  • Union operation is both commutative and associative.

Example:

Consider the following two relations A and B,

Relation A 

And Relation B 

Then, A ∪ B is

2. Cartesian/CROSS Product

Cross product is a way of combining two tables. The resulting table will contains each of the attributes in both tables being combined.

It is denoted by ‘✕’ symbol

If A and B are two tables and needs to a cross product between them then it will be given below

A ✕ B, Where A and B are the two tables,

Example:

Consider following tables  

“Student” Table

And “Student_Detail” Table

On applying CROSS PRODUCT on STUDENT and Student_Detail tables is given below

Important Terms

The cardinality (Number of Tuples/Rows):
Number of Tuples after Cross product = Rows of A table + Rows of B table

Degree (No of Columns)
Number of columns after Cross product = columns of A table  X columns of B table

In the above table We can see that the number of tuples (Rows) in STUDENT relation is 2, and the number of tuples in Student_DETAIL table is 2.

  • So the number of tuples in the resulting table after performing CROSS PRODUCT is 2 x 2 = 4.
  • Number of columns will be the sum of total columns in both tables so, 3+2=5

3. Difference Operator (-)

Let A and B be two relations.

Then

  • A – B is the set of all tuples belonging to A and not to B.
  • In A – B, duplicates are automatically removed.
  • Difference operation is associative but not commutative.

Example

Consider the following two relations A and B

Relation A

Relation B

Then, A – B is

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