What are Venn diagrams?
A Venn diagram is a rectangle representing the whole space and circles inside representing various subspaces.
For example, A could represent the event that a person had blue eyes. Event B could be that person have brown hair.
Events on a Venn diagram
This Venn diagram shows the complement of A. The part shaded with diagonal lines is everything that is not in A and we call this the complement. Note the spelling – it doesn’t say ‘compliment’ as charming as event A might be. See Example 1. The complement of A is written as:
In this Venn diagram we see the union of events A and B. This means that the shaded part represents all outcomes where either event A or event B has occurred. See Example 2. The union of A and B is written as:
Alternatively to the union, there is also the intersection of two events. The intersection represents the set of all outcomes where BOTH events A and B have occurred. See Example 3. The intersection of A and B is written as:
It follows from the three previous definitions that it is possible to combine complement, union or intersection to get particular areas of a Venn diagram. See Example 4. The above combination is written as: