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:
“Birth dates and bathroom scales tell more truth than I want to know.”
—Mason Cooley (b. 1927)
“How to attain sufficient clarity of thought to meet the terrifying issues now facing us, before it is too late, is ... important. Of one thing I feel reasonably sure: we can’t stop to discuss whether the table has or hasn’t legs when the house is burning down over our heads. Nor do the classics per se seem to furnish the kind of education which fits people to cope with a fast-changing civilization.”
—Mary Barnett Gilson (1877–?)