truth table


A truth tableMathworldPlanetmath is a tabular listing of all possible input value combinationsMathworldPlanetmathPlanetmath for a logical function and their corresponding output values. Similarly, the truth table of a logical propositionPlanetmathPlanetmathPlanetmath is the truth table of the corresponding logical function.

For instance, the truth table of the connectiveMathworldPlanetmath “or” is as follows:

a b ab
F F F
F T T
T F T
T T T

For n input variables, there will always be 2n rows in the truth table. A sample truth table for “(ab)c” would be

a b c (ab)c
F F F T
F F T F
F T F T
F T T F
T F F T
T F T F
T T F T
T T T T

(Note that represents logical and, while represents the conditional truth function).

To compute truth tables of expressions, one often proceeds in steps. for instance, to compute a truth table for “¬p(pq), one might proceed as follows:

p q ¬p (pq) ¬p(pq)
F F T F T
F T T F T
T F F F F
T T F T T

For reference, here is a truth table of some popular connectives:

p q pq pq pq pq pq
F F F F F T T
F T T F T T F
T F T F T F F
T T T T F T T

For completeness, here are the remaining connectives, excluding trivial connectives which depend on only one or none of their arguments:

p q pq pq pq p↛q pq
F F T T T F F
F T T F F F T
T F T F T T F
T T F F T F F
Title truth table
Canonical name TruthTable
Date of creation 2013-03-22 11:54:35
Last modified on 2013-03-22 11:54:35
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 16
Author rspuzio (6075)
Entry type Definition
Classification msc 03-00
Classification msc 34C29
Related topic ZerothOrderLogic
Related topic PropositionalCalculus