Definition:Truth Table/Matrix Presentation

Definition

A two-element truth table can be presented in matrix form:

$\begin{array}{c|cc} \implies & \T & \F \\ \hline \T & \T & \F \\ \F & \T & \T \\ \end{array}$$\qquad$$\begin{array}{c|cc} \land & \T & \F \\ \hline \T & \T & \F \\ \F & \F & \F \\ \end{array}$$\qquad$$\begin{array}{c|cc} \lor & \T & \F \\ \hline \T & \T & \T \\ \F & \T & \F \\ \end{array}$$\qquad$$\begin{array}{c|cc} \iff & \T & \F \\ \hline \T & \T & \F \\ \F & \F & \T \\ \end{array}$

that is, in the form of a Cayley table.

This, however, can be used only when the operation being displayed has two elements.

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $3$ Truth-Tables