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:
“Truth is a pain which will not stop. And the truth of this world is to die. You must choose: either dying or lying. Personally, I have never been able to kill myself.”
—Louis-Ferdinand Céline (1894–1961)
“But hospitality must be for service, and not for show, or it pulls down the host. The brave soul rates itself too high to value itself by the splendor of its table and draperies. It gives what it hath, and all it hath, but its own majesty can lend a better grace to bannocks and fair water than belong to city feasts.”
—Ralph Waldo Emerson (1803–1882)