Definition:Truth Table

Definition
A truth table is a tabular array that represents the computation of a truth function, that is, a function of the form:
 * $f : \mathbb B^k \to \mathbb B$

where:
 * $k$ is a non-negative integer
 * $\mathbb B$ is a set of truth values, usually $\left\{{0, 1}\right\}$ or $\left\{{T, F}\right\}$.

Matrix Presentation
Some sources prefer to present two-element truth tables in matrix form, for example:


 * $\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 & F & T \\ F & T & F \\ \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.

Also known as
Some sources hyphenate: truth-table.

Also see

 * Results proved using truth tables can be found here.