# Sets Intersection: Intersection Of Two Sets

In these lessons, we will learn how to use Venn Diagrams to illustrate the intersection of two sets.

Related Topics:

More lessons on Sets

Intersection of Three Sets

Venn Diagrams

The **intersection** of two sets *X* and *Y* is the set of elements that are common to both set *X* **and** set *Y*. It is denoted by *X* ∩ *Y* and is read ‘*X* intersection *Y*’.

**Example: **

Draw a Venn diagram to represent the relationship between the sets

*X* = {1, 2, 5, 6, 7, 9, 10} and *Y* = {1, 3, 4, 5, 6, 8, 10}

**Solution: **

We find that *X* ∩ *Y* = {1, 5, 6, 10} ← in both *X* and *Y *

For the Venn diagram,

** Step 1** : Draw two overlapping circles to represent the two sets.

** Step 2** : Write down the elements in the intersection.

** Step 3** : Write down the remaining elements in the respective sets.

Notice that you start filling the Venn diagram from the elements in the intersection first.

**If *** X *** ⊂***Y *then* X*** ∩***Y* = *X** . * We will illustrate this relationship in the following example.

**Example: **

Draw a Venn diagram to represent the relationship between the sets

* X* = {1, 6, 9} and *Y* = {1, 3, 5, 6, 8, 9}

**Solution:**

We find that *X* ∩ *Y* = {1, 6, 9} which is equal to the set *X*

For the Venn diagram,

** Step 1** : Draw one circle within another circle

** Step 2** : Write down the elements in the inner circle.

** Step 3** : Write down the remaining elements in the outer circle.

## Videos

Venn diagrams are an important tool allowing relations between sets to be visualized graphically.
This video introduces the use of Venn diagrams to visualize intersections and unions of sets, as well
as subsets and supersets.

#### Venn Diagrams, Unions, and Intersections

Venn diagrams are an important tool allowing relations between sets to be visualized graphically.
This lesson introduces the use of Venn diagrams to visualize intersections and unions of sets, as well
as subsets and supersets.

#### Intersection of Sets

The following video describes the Union and Intersection of Sets.

#### Sets: Union, Intersection, Complement

#### Sets: Union and Intersection

The basic idea of the 'union' and 'intersection' of two sets.