Venn diagrams with three subsets
It is possible to have Venn diagrams with three subsets.
Example
A set of pupils were asked which sports they played in school.
They were given the following options: Football, Hockey, Netball or None.
Here is a list of sports they played:
| Sport | Name |
| Football | Thomas, Sean, Chris, Sarah, Freya, Sophie |
| Hockey | Noah, Thomas, Chris, Sophie, Jayne |
| Netball | Carrie, Sophie, Jayne, Alex, Freya |
| None | Melanie |
| Sport | Football |
|---|---|
| Name | Thomas, Sean, Chris, Sarah, Freya, Sophie |
| Sport | Hockey |
|---|---|
| Name | Noah, Thomas, Chris, Sophie, Jayne |
| Sport | Netball |
|---|---|
| Name | Carrie, Sophie, Jayne, Alex, Freya |
| Sport | None |
|---|---|
| Name | Melanie |
Draw a Venn diagram to show the information.
Solution
The diagram shows us clearly who plays which sports, and also includes the pupils who do not play any sports, by placing their names outside of the circles.
Universal set
Universal set contains all the elements that we are interested in at the moment.
\(ε\) = {sean, sarah, freya, chris, thomas, sophie, noah, jayne, carri, alex and melanie}
Question
Carys and Maia are going on holiday.
Carys has the following items to take with her: Hairdryer, straighteners, travel iron, travel adapter.
Maia can take the following items: Hairdryer, curling tongs, mosquito plug.
They both have mobile phones, which they are going to use to listen to music. Maia is taking a docking station for her phone which Carys can also use.
Just In magazine has a list of must-have electrical items on holiday. They are:
- Mobile charger
- Headphones
- Camera
- Camera charger
- Travel adaptor
- Mosquito plug
- Travel iron
- Hairdryer
- Curling tongs
- Digital music player
Complete the Venn diagram to ensure they have packed the essentials on the Just In list.
No, they haven’t packed the essentials on the Just In list as they don’t have a camera, mobile phone charger or camera charger.
