## 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.