Definition:Fundamental Truth Table

Jump to navigation Jump to search

Definition

The fundamental truth tables are the characteristic truth tables for:

Logical Not
Conjunction
Disjunction
Conditional
Biconditional

as follows:

Logical Not

The characteristic truth table of the negation operator $\neg p$ is as follows:

$\begin{array}{|c||c|} \hline p & \neg p \\ \hline \F & \T \\ \T & \F \\ \hline \end{array}$

Conjunction

The characteristic truth table of the logical conjunction operator $p \land q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \land q \\ \hline \F & \F & \F \\ \F & \T & \F \\ \T & \F & \F \\ \T & \T & \T \\ \hline \end{array}$

Disjunction

The characteristic truth table of the logical disjunction operator $p \lor q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \lor q \\ \hline \F & \F & \F \\ \F & \T & \T \\ \T & \F & \T \\ \T & \T & \T \\ \hline \end{array}$

Conditional

The characteristic truth table of the conditional (implication) operator $p \implies q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \implies q \\ \hline \F & \F & \T \\ \F & \T & \T \\ \T & \F & \F \\ \T & \T & \T \\ \hline \end{array}$

Biconditional

The characteristic truth table of the biconditional operator $p \iff q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \iff q \\ \hline \F & \F & \T \\ \F & \T & \F \\ \T & \F & \F \\ \T & \T & \T \\ \hline \end{array}$

Historical Note

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