Venn diagrams

Venn diagrams are named after John Venn who wrote about them in 1880. He didn’t invent them but he gathered all that was known about them and described how they are used. They are very similar to Euler diagrams, invented by Leonhard Euler, one of the greatest mathematicians of all time from Switzerland.

To understand Venn diagrams you first need to know what a set is.

A set is a collection of distinct objects. These objects can be anything: numbers, types of car, colours, playing cards, sports etc.

An example of a set is all of the numbers you can roll on a 6-sided dice. This set consists of the numbers 1, 2, 3, 4, 5 and 6. Each of these numbers is distinct, separate from the others and each belongs to the set of numbers that can be rolled on a dice.

Sets are written like this, between curly brackets. {1, 2, 3, 4, 5, 6}. Usually a set is given a name, often a single letter. The set of numbers you can roll on a six sided dice could be labelled D and written like this.

D = {1, 2, 3, 4, 5, 6}

Another set could be sports that are played with a ball in school. This set could include football, hockey, tennis, netball, rugby, cricket and so on. If a particular school only offered these six sports then the set of sports played with a ball at that school could be labelled S and written like this.

S = {football, hockey, tennis, netball, rugby, cricket}

These sets can be shown inside circles like this

It is clear that these two sets do not overlap in any way. None of the numbers that you can roll on a dice are also sports that you can play with a ball.

Some sets do overlap though. We looked earlier at two sets in a pack of cards, 7s and clubs and we saw that these sets overlap. When two sets overlap, the members that are in both sets are called the intersection.

If a member belongs to one set AND another set then it belongs to the INTERSECTION of the two sets.

All clubs and all sevens can be found in the union of the set of clubs and the set of sevens.

If a member belongs to one set OR another set then it belongs to the UNION of the two sets.