Intro to DBMS

Binary Operators in Relational Algebra

All those Operators that 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

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

  • It is denoted by ‘✕’ symbol

If A and B are two tables and need 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

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 the STUDENT relation is 2, and the number of tuples in the Student_DETAIL table is 2.

  • So, the number of tuples in the resulting table after performing CROSS PRODUCT is 2 x 2 = 4.
  • The number of columns will be the sum of the 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