Venn Diagrams

What is a Venn Diagram?  The Venn diagram was introduced by John Venn.  It is a diagram that shows all possible logical relations between a finite collection of sets.  A Venn diagram consists of overlapping circles. Each circle contains all the elements of a set. Where the circles overlap shows the elements that the sets have in common. Generally there are two or three circles.  Sounds a little complicated and can look that way too!

A 5 set Venn diagram

The intersection of the Greek, Latin and Russian alphabet.

Lets start with a couple definitions and some examples to see if we can make this less complicated.
A set is a collection of objects.
A ∩ B is the intersection of two sets or all items common to A and B.

How are Venn diagrams useful in math? Venn diagrams enable students to organize information visually so they are able to see the relationships between sets of items.

 
Venn diagrams can be used for to compare other sets too.  Lets discuss its use in the life of a College Student.
Let A = enough sleep, B = social life and C = good grades.
Then,
A ∩ B = Slacker
B ∩ C = Zombie
A ∩ C = Nerd
and A ∩ B ∩ C = Defies the Laws of Physics

This can be shown in the following Venn Diagram.


















Lets try another example involving food.

If A = Flour, B = Egg and C = Milk
Then, 
A ∩ B = Pasta
A ∩ C = Batter
B ∩ C = Omelette
and
A ∩ B ∩ C = Pancakes