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 often credited with their invention in the Tractatus Logico-Philosophicus.
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Famous quotes containing the words truth and/or table:
“Pleasure cannot be shared; like Pain, it can only be experienced or inflicted, and when we give pleasure to our Lovers or bestow Charity upon the Needy, we do so, not to gratify the object of our Benevolence, but only ourselves. For the Truth is that we are kind for the same reason as we are cruel, in order that we may enhance the sense of our own Power.”
—Aldous Huxley (1894–1963)
“The gingham dog and the calico cat
Side by side on the table sat;”
—Eugene Field (1850–1895)