# Relational Algebra - Intersect operator (intersection)

intersect (or intersection) is a relational operator that returns the intersection of two relation A and B, denoted by A ∩ B.

An intersection is defined as all tuples (rows) that are present in both of two union-compatible (same columns and same type) relation A and B.

The following definition are also equivalent.

• all elements of A that also belong to B
• all elements of B that also belong to A

## Syntax

### Minus

A derived operator using minus (-) where the minus expression $( R1 - R2 )$ returns anything that is only in R1

$$\Large R1 \cap R2 = R1 - ( R1 - R2 )$$

### Join

• Derived using join

$$\Large R1 \cap R2 = R1 \times R2$$