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:
“As a child I was taught that to tell the truth was often painful. As an adult I have learned that not to tell the truth is more painful, and that the fear of telling the truth—whatever the truth may be—that fear is the most painful sensation of a moral life.”
—June Jordan (b. 1936)
“When I think of our lands I think of the house
And the table that holds a platter of pears,
Vermilion smeared over green, arranged for show.”
—Wallace Stevens (1879–1955)