# Sets Intersection: Intersection Of Two Sets

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

### Venn Diagrams Of Two Sets

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

To draw 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. #### Venn Diagrams, Unions, And Intersections

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.

#### Sets: Union, Intersection, Complement

Example:
U = {7,8,9,10,11,12,13}
A = {8,10,12}, B = {10,12,13}, C = {7,8}
Find
A ∪ B
A ∩ B
A ∪ B'
(A ∪ B') ∩ C

#### Sets: Union and Intersection

The basic idea of the ‘union’ and ‘intersection’ of two sets.
The intersection of two sets are those elements that belong to both sets.
The union of two sets are all the elements for both sets.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 