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

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More Topics on Sets

A

**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.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.