# Definition:Fiber of Truth/Solution

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## Definition

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

Let $S = \map {P^{-1} } \T$ be the **fiber of truth (under $P$)**.

Then an element of $S$ is known as a **solution** of $P$.

This terminology is usual when $P$ is an equation in the context of algebra.

## Also known as

A **solution of $P$** can also be seen (including on $\mathsf{Pr} \infty \mathsf{fWiki}$) as a **solution to $P$**.

## Sources

- 1963: Morris Tenenbaum and Harry Pollard:
*Ordinary Differential Equations*... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $3$: The Differential Equation