Definition:Fundamental Truth Table

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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.


Sources