Inclusion relation

Power set

The inclusion relation${\displaystyle \subseteq }$ is a partial order on the set ${\displaystyle {\mathcal {P}}(S)}$ defined by ${\displaystyle A\leq B\iff A\subseteq B}$. We may also partially order ${\displaystyle {\mathcal {P}}(S)}$ by reverse set inclusion by defining ${\displaystyle A\leq B{\text{ if and only if }}B\subseteq A.}$