Definition:Fiber of Truth

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

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

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

Linguistic Note
The phrase fiber of truth (with the same meaning) is occasionally seen in natural language.

In particular:
 * "... to extract the fiber of truth from this tissue of lies ..."

sounds as though it would be used in the context of the courtroom by a lawyer waxing rhetorical.

The British English spelling of fiber is fibre. The pronunciation is the same.

Also see

 * Definition:Support of Characteristic Function