# Use Venn diagrams to sort data

## Home learning focus

Learn about using Venn diagrams to sort data and recognise the terms 'universal set', 'member' and 'complement'.

This lesson includes:

• two videos
• a learning summary

Created in partnership with GCSEPod

# Learn

## Venn diagrams

Venn diagrams are used to sort groups of data. They consist of 2 or more circles, often overlapping, contained inside a rectangle, like in the image here.

Each circle within the diagram represents a set. The information in a set could be made up of a list of numbers, for example, or follow a certain rule or have a specific property.

A Venn diagram is used to show the relationship between the different items shown in a number of sets. These items are known as elements or members of a set.

Example - Lemons and bananas

You could use a Venn diagram to show the differences and similarities between lemons and bananas. You would have a set showing the elements of lemons, another set showing the elements of bananas, and the overlap showing the set of shared elements.

Numbers can also be sorted into a Venn diagram. Where the numbers are placed on the diagram depends on the properties of the numbers. Each number shown is an element or a member of the set it belongs in.

A set of numbers can be defined by a rule, or could simply be a list of numbers. Sometimes the only thing that the numbers in a set have in common is that they belong to a set with a particular name.

When the set of numbers with a shared rule, or shown as a list, that need to be placed in a Venn diagram are written out, they are contained within curly brackets, like these: { ... }.

Examples

• Set E = {Odd numbers} - this set of numbers is defined by a rule. In this case, all the numbers in 'set E' are odd.

• Set F = {2, 4, 5, 9, 10} - this set of numbers does not follow a specific rule, and it does not matter why they are in the set.

• Set G = {1,2,3...10} - this set is the integers, or whole numbers, from 1 up to, and including, 10.

Using '...' is a shorter way of writing the set, instead of having to write it out in full, ie 'Set G = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}'.

Watch up to 1:33 in this short video from GCSEPod to learn more about sorting data into a Venn diagram.

## The universal set and complement of a set

The universal set refers to all the values that need to be considered in a particular question. The universal set is often represented by the Greek letter epsilon, ε. All the members of the universal set must be represented somewhere inside the rectangle in a Venn diagram.

The complement of a set refers to all the elements which are not in a particular set. It is represented as the name of the set, followed by a dash. For example A’ is the set of elements which are not in set A.

Example

Consider the universal set ε = {1, 2, 3, 4, 5, 6, 7, 8, 9}

This means that all the numbers shown within the curly brackets must be considered and placed in one of the sections of the Venn diagram.

All the numbers from the universal set are displayed somewhere within the rectangle, or within one or both of the circles.

Set A = {Even numbers} means that all the numbers which are in the circle marked A are even.

Set B = {Prime numbers} means that all the numbers which are in the circle marked B are prime.

The overlap section will be the numbers that are both even and prime - in this case it's number 2.

We can write out the complements of Set A and Set B by looking at the values which are not in each set, eg

A’ = {1, 3, 5, 7, 9} because these elements are not in Set A.

B’ = {1, 4, 6, 8, 9} because these elements are not in Set B.

Watch this next short video from GCSEPod to learn more about some of the vocabulary used when working with Venn diagrams.

# Practise

## Activity 1

Quiz: Use Venn diagrams to sort data

Think you know about Venn diagrams and the words related to them? Practise what you have learned in this lesson with this quiz from GCSEPod. There are 9 questions in total, with multiple-choice answers. Write your answer choice on a piece of paper, referring back to the information in the videos if you need to.