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.
Venn diagrams can be used to illustrate the union, intersection, and complements of sets.
These Venn diagrams show the union (upper left), intersection (upper right), and compliment (second row) of sets.
Use a Venn diagram to illustrate [latex](H \cap F)^{c} \cap W[/latex].
We’ll start by identifying everything in the set [latex]H \cap F[/latex].
Now, [latex](H \cap F)^{c} \cap W[/latex] will contain everything not in the set identified above that is also in set [latex]W[/latex].
Create an expression to represent the outlined part of the Venn diagram shown.
The elements in the outlined set are in sets [latex]H[/latex] and [latex]F[/latex], but are not in set [latex]W[/latex]. So we could represent this set as [latex]H \cap F \cap W^c[/latex].
