Subsets and membership

\(A\subseteq B\) means every element of A belongs to B; equality is allowed. \(A\nsubseteq B\) means that at least one element of A lies outside B. A nested Venn region represents containment.

Example

For \(A=\{4,8\}\) and \(B=\{2,4,6,8,10\}\), \(A\subseteq B\). Also \(A\subseteq A\). Since \(2\in B\) but \(2\notin A\), \(B\nsubseteq A\).

Use \(\in\) between an element and a set; use \(\subseteq\) between sets. Here \(4\in A\), \(\{4\}\subseteq A\), and \(\{4\}\notin A\). The empty set is a subset of every set.