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:
“It is a pleasure to stand upon the shore, and to see ships tossed upon the sea: a pleasure to stand in the window of a castle, and to see a battle and the adventures thereof below: but no pleasure is comparable to standing upon the vantage ground of truth ... and to see the errors, and wanderings, and mists, and tempests, in the vale below.”
—Francis Bacon (1561–1626)
“The table kills more people than war does.”
—Catalan proverb, quoted in Colman Andrews, Catalan Cuisine.