To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called Venn Diagrams.
Venn Diagram
A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.
Basic Venn diagrams can illustrate the interaction of two or three sets.
Example 9
Create Venn diagrams to illustrate A∪B,A∩B, and Ac∩B
A∪B contains all elements in either set.
A∪B contains all elements in either set.
A∩B contains only those elements in both sets - in the overlap of the circles.
Example 10
Use a Venn diagram to illustrate (H∩P)c∩W
We'll start by identifying everything in the set H∩P
Now, (H∩P)c∩W will contain everything not in the set identified above that is also in set W
Example 11
Create an expression to represent the outlined part of the Venn diagram shown.
The elements in the outlined set are in sets H and F, but are not in set W. So we could represent this set as H∩F∩W
Try it Now 3
Create an expression to represent the outlined portion of the Venn diagram shown