Set Theory: Venn Diagrams



A Venn Diagram is a pictorial representation of the relationships between sets.

Related Topics:
More lessons on Sets & Venn Diagrams

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 labelled 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 : 2x – 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.
2x – 3 < 11 ⇒ 2x < 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.







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