**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

- 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**

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__

__Example__

Consider the following two relations: A and B

**Relation A**

**Relation B**

Then, A – B is