**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

- Union Operators
- Cross Product
- 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: __

__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__

__Example__

Consider the following two relations A and B

**Relation A**

**Relation B**

Then, A – B is