Truth table

related topics
{math, number, function}
{style, bgcolor, rowspan}
{theory, work, human}
{system, computer, user}

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid.

Practically, a truth table is composed of one column for each input variable (for example, A and B), and one final column for all of the possible results of the logical operation that the table is meant to represent (for example, A XOR B). Each row of the truth table therefore contains one possible configuration of the input variables (for instance, A=true B=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is credited with their invention in the Tractatus Logico-Philosophicus[1] although Peirce and Jevons are suggested to have been aware of them before.[2]


Full article ▸

related documents
Halting problem
Subset sum problem
Uniform space
Taylor series
Lp space
Fermat number
Support vector machine
Multiplication algorithm
Ackermann function
BCH code
Basis (linear algebra)
Stochastic process
Sorting algorithm
Fundamental theorem of algebra
Dual space
Euler's formula
Primitive recursive function
Continuous function
Bessel function
Vacuous truth
Probability theory
Lie algebra
Hyperreal number
Monte Carlo method
Fundamental group
Computable number
Multivariate normal distribution