Set Theory: Universal Set

In this lesson, we will learn what is a Universal set and how it may be represented in a Venn Diagram.

Related Topics:
More Topics on Sets

A universal set is the set of all elements under consideration, denoted by capital U or sometimes capital E.


Given that U = {5, 6, 7, 8, 9, 10, 11, 12}, list the elements of the following sets.

a) A = {x : x is a factor of 60}
b) B = {x : x is a prime number}


The elements of sets A and B can only be selected from the given universal set U .

a) A = {5, 6, 10, 12}
b) B = {5, 7, 11}

In Venn diagrams, the universal set is usually represented by a rectangle and labelled U.


Draw a Venn diagram to represent the following sets:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 5, 6}, B = {3, 9}


Step 1 : Draw a rectangle and label it U to represent the universal set.

Step 2 : Draw circles within the rectangle to represent the other sets. Label the circles and write the relevant elements in each circle.

Step 3 : Write the remaining elements outside the circles but within the rectangle.


Universal Sets Videos

Learn about universal sets.

Universal set and absolute complement


OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

OML Search