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Set Theory: Universal Set




 
In these lessons, we will learn what is a universal set and how it may be represented in a Venn Diagram.

Related Topics:
More Topics on Sets

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


Example:

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}

Solution:

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 labeled U.


Example:

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}

Solution:

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 set




Universal Sets Videos

Learn about universal sets.
Universal set and absolute complement


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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