Create and Read Venn Diagrams

If you saw the following diagram, what do you think it could mean?

 

 

Well, we can see that there is 'Rugby' written by the left circle and 'Football' next to the right one.

 

So perhaps it's about what sports students in one class take part in?

If so, then we can see that 8 students play both football and rugby.

We call where the two circles overlap the intersection.

 

There are 10 students inside the rugby circle that are not in the intersection.

That must mean that 10 students play rugby only!

 

Can you already tell how many students play only football?

That's right, it's 12!

 

 

Finally, we have the number 5 floating in the rectangle - what could that mean?

 

Well, we can see that the 5 is in neither circle.

So it must mean that 5 students play neither football nor rugby.

 

If we look at the diagram one more time, how could we find out how many students play rugby or football?

 

 

Well, that's all the numbers in the circles added together!

10 + 8 + 12 = 30 students play rugby or football.

We call this the union.

 

One thing to note here - in maths, when we say 'or', we don't mean 'either ... or ...'

Rather, we mean '... or ... or both'

That's why the union includes the 8 in the intersection!

 

 

We call diagrams like the one above Venn diagrams.

 

Ready to do some questions on them?!