Let $V$ be a set and let $P$ be a property, such that for no $F\subseteq V, \ P(F)$ is true.
Is then $\left\{ F\subseteq V | P(F) \right\} = \emptyset$ or $= \left\{ \emptyset \right\} $ ?
Let $V$ be a set and let $P$ be a property, such that for no $F\subseteq V, \ P(F)$ is true.
Is then $\left\{ F\subseteq V | P(F) \right\} = \emptyset$ or $= \left\{ \emptyset \right\} $ ?
If $A=\{F\subseteq V\mid P(F)\}=\{\varnothing\}$ then it means that $\varnothing\in A$, therefore $P(\varnothing)$ is true.
If no set is such that the property holds, then $A=\varnothing$, i.e. it has no elements.