## 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.