# Definition:Derivative Truth Table

## Definition

A **derivative truth table** is a truth table for a statement form which is not mapped by one of the fundamental truth tables:

## Historical Note

The separate categorization of the five fundamental truth tables for the five statement forms appears in 1946: Alfred Tarski: *Introduction to Logic and to the Methodology of Deductive Sciences*, and may be idiosyncratic.

This treatment refers to all statement forms which are not one of these five as **compound**, but $\mathsf{Pr} \infty \mathsf{fWiki}$ follows the conventional view that a compound statement is **any** statement which involves a logical connective.

Following Tarski's lead, a **derivative truth table** can therefore be defined as a truth table for a compound statement.

The distinction is not an important one, but such a treatment can be useful for beginners.

## Sources

- 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S \text{II}.13$: Symbolism of sentential calculus