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.
Read more about Truth Table: Applications
Famous quotes containing the words truth and/or table:
“I am sometimes told that “Women aint fit to vote. Why, don’t you know that a woman had seven devils in her: and do you suppose a woman is fit to rule the nation?” Seven devils aint no account; a man had a legion in him.”
—Sojourner Truth (c. 1797–1883)
““A sigh for every so many breath,
And for every so many sigh a death.
That’s what I always tell my wife
Is the multiplication table of life.””
—Robert Frost (1874–1963)