Venn diagrams – WJECThree or more sets in a Venn diagram

It's possible a Venn diagram can have three (or more) sets depicted within them.

Example

A set of pupils were asked which sports they played in school, from a list of Football, Hockey, Netball and None.

The full list of pupils forms the universal set U {thomas, sean, chris, sarah, freya, sophie, noah, melanie, jayne, carrie, alex}

There are then three more sets to consider.

Football = {thomas, sean, chris, sarah, freya, sophie}

Hockey = {noah, thomas, chris, sophie, jayne}

Netball = {carrie, sophie, jayne, alex, freya}

None = {melanie}

All of this information can be easily represented on a Venn diagram:

• The section that Sophie is in would be F ∩ H ∩ N, ie the intersection of all three sets.
• To describe the section of the Venn diagram that Freya is in we would write F ∩ N - F ∩ H ∩ N, ie the intersection of football and netball minus the intersection of all three.
• We could also describe the section that Freya is in as F ∩ N ∩ H', ie the intersection of the set for football and netball and not in hockey.