Definition:Fiber of Truth

Definition
Let $P: X \to \set {\mathrm T, \mathrm F}$ be a propositional function defined on a domain $X$.

The fiber of truth (under $P$) is the preimage, or fiber, of $\mathrm T$ under $P$:
 * $\set {x \in X: \map P x = \mathrm T}$

That is, the elements of $X$ whose image under $P$ is $\mathrm T$.

Also known as
The fiber of truth is often referred to also as the solution set for $P$.

This is particularly the case in mathematical contexts.

Also see

 * Definition:Support of Characteristic Function