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.