# Set Theory: Venn Diagrams

Related Topics:

More lessons on Sets
Intersection of Two Sets
Intersection of Three Sets
**What is a Venn Diagram?**
A Venn Diagram is a pictorial representation of the relationships between sets.

We can represent sets using

**Venn diagrams**. In a Venn diagram, the sets are represented by shapes; usually circles or ovals. The elements of a set are labeled within the circle.

**Example: **

Given the set *P* is the set of even numbers between 15 and 25. Draw and label a Venn diagram to represent the set *P* and indicate all the elements of set *P* in the Venn diagram.

**Solution: **

List out the elements of *P*.

* P = * {16, 18, 20, 22, 24} ← ‘between’ does not include 15 and 25

Draw a circle or oval. Label it *P* . Put the elements in *P*.

**Example: **

Draw and label a Venn diagram to represent the set

*R *= {Monday, Tuesday, Wednesday}.

**Solution: **

Draw a circle or oval. Label it *R* . Put the elements in *R*.

**Example: **

Given the set *Q* = {*x* : 2*x* – 3 < 11, *x* is a positive integer }. Draw and label a Venn diagram to represent the set *Q*.

**Solution: **

Since an equation is given, we need to first solve for *x*.

2*x* – 3 < 11 ⇒ 2*x* < 14 ⇒ *x* < 7

So, *Q* = {1, 2, 3, 4, 5, 6}

Draw a circle or oval. Label it *Q* .

Put the elements in *Q*.

## Venn Diagram Videos

What's a Venn Diagram, and What Does Intersection and Union Mean?

#### Venn Diagram two Subsets

Learn about Venn diagrams with two subsets.

#### Venn Diagram Two Subsets Using Regions

Learn about Venn diagrams with two subsets using regions.

#### Venn Diagrams With Three Subsets

Learn about Venn diagrams with three subsets.