Consider [set](Sets.md) $A$ and $B.$ A _subset_ $B$ is a set that contains either _some_ or _all_ the same elements as the set $A.$ This is denoted as $B\subset A$ in the case where $B$ is a _proper subset_ of $A$ and $B\subseteq A$ if it is the case that the statement $A=B$ might be true. To indicate that a third set, $C$ is _not_ a proper subset of $A$ we write $C\not\subset A.$ If it is not a subset of $A$ or equal to $A$ we write $C\not\subseteq A.$ ^ef52c7 # Equivalent sets Given [sets](Sets.md) $A$ and $B,$ if $B\subseteq A$ and $A\subseteq B$ then $A=B.$ # Empty subsets The [null set](The%20null%20set.md) is a [subset](Subsets.md) of every [set](Sets.md) and a [proper subset](Subsets#^ef52c7) of every set except for the null set. %%This is intuitvely true, but please also note down a source that states this as well as possibly explain this unless it's truly trivial.%% #MathematicalFoundations/SetTheory