Definition:Particular Negative/Set Theory

Definition
The particular negative $\exists x: S \left({x}\right) \land \neg P \left({x}\right)$ can be expressed in set language as:


 * $\left\{{x: S \left({x}\right)}\right\} \cap \left\{{x: \neg P \left({x}\right)}\right\} \ne \varnothing$

or, more compactly:


 * $S \cap \complement \left({P}\right) \ne \varnothing$

Also see

 * Equivalence of Definitions of Particular Negative


 * Definition:Square of Opposition


 * Definition:Universal Affirmative/Set Theory
 * Definition:Universal Negative/Set Theory
 * Definition:Particular Affirmative/Set Theory