\begin{definition}[Definition:Particular Affirmative/Set Theory]
The particular affirmative $\exists x: \map S x \land \map P x$ can be expressed in set language as:
:$\set {x: \map S x} \cap \set {x: \map P x} \ne \O$
or, more compactly:
:$S \cap P \ne \O$
\end{definition}