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Sets and Venn Diagrams

Sets are very useful for displaying information that separates into categories.
The following notation is used.
\[A \subset B\]
-  
\[A\]
  is a subset of  
\[B\]

\[A \subseteq B\]
-  
\[A\]
  is a subset of  
\[B\]
  and may be equal to  
\[B\]
.
\[A \cup B\]
- the set of elements in either  
\[A\]
  or  
\[A\]

\[A \cap B\]
- the set of elements in both  
\[A\]
  and  
\[A\]

\[\mathscr{E}\]
- everything in all categories.
Suppose we have sets  
\[A, \: B, \: C\]
  satisfying
\[A= \{0,2,4,6,8 \}\]

\[B= \{1,2,3,4 \}\]

\[C= \{0,1,4,9 \}\]

\[\mathscr{E}=\{0,1,2,3,4,5,6,7,8,9,10 \}\]
We can display this on a diagram, called a Venn diagram.

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