Definition:Fiber of Truth

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

The fiber of truth (under $P$) is the preimage, or fiber, of $\T$ under $P$:
 * $\map {P^{-1} } \T := \set {x \in X: \map P x = \T}$

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

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.

Some sources denote the fiber of truth under $P$ as $\sqbrk {\size P}$.

Also see

 * Definition:Support of Characteristic Function