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 stranger than fiction, but it is because Fiction is obliged to stick to possibilities; Truth isn’t.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Life is a thin narrowness of taken-for-granted, a plank over a canyon in a fog. There is something under our feet, the taken-for-granted. A table is a table, food is food, we are we—because we don’t question these things. And science is the enemy because it is the questioner. Faith saves our souls alive by giving us a universe of the taken-for-granted.”
—Rose Wilder Lane (1886–1968)