# Subset **A [[set]] which contains elements all of which are also in another set.** ![[Subset.svg|250]] *$A$ is a subset of $B$; $B$ is a superset $A$* > [!Example] Subset and superset > If $A$ is a *subset* of $B$, then[^1] > $A\subseteq B, A\subset B$ > Additionally, $B$ would then be the *superset* of $A$ and[^1] > $B\supseteq A, B\supset A$ ^5c54ca > [!Example] Proper subset and proper superset > If $A$ is a subset of $B$, but is *not equal* to $B$, then > - $A$ is a *proper subset* of $B$ > - $B$ is a *proper superset* of $A$.[^1] > $A\subsetneq B, B\subsetneq A$ The relation symbolised by $\subseteq$ is known as *inclusion* or *containment*. The [[Set#^5f880b|empty set]] is a subset of *every set* and every set is a *subset of itself*. $\varnothing\subseteq A, A\subseteq A$ [^1]: Some authors may use $\subset$ and $\supset$ to indicate a *proper subset* and *proper superset* instead.