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 remarkable that, notwithstanding the universal favor with which the New Testament is outwardly received, and even the bigotry with which it is defended, there is no hospitality shown to, there is no appreciation of, the order of truth with which it deals. I know of no book that has so few readers. There is none so truly strange, and heretical, and unpopular. To Christians, no less than Greeks and Jews, it is foolishness and a stumbling-block.”
—Henry David Thoreau (1817–1862)
“They were not on the table with their elbows.
They were not sleeping in the shelves of bunks.
I saw no men there and no bones of men there.”
—Robert Frost (1874–1963)