Truth table Glossary
Definition
A truth table is simply a way of representing a truth function in the form of a look-up table giving the value of the function for each combination of inputs.
Comments
Each truth-functional connective has its truth table. Moreover, every formula of propositional logic expresses a truth function, so every formula has a truth table as well.
Truth tables of any arity can generally be written as columns of values. However, for binary operations including the standard binary connectives we usually write them in a square matrix format with rows corresponding to values of the left subformula and columns corresponding to values of the right one.
Examples
-
Conjunction has the truth
table:
AND 0 1 0 0 0 1 0 1 -
The formula p IFF (q
IFF NOTr) has the truth table:
p q r p IFF (q IFF NOTr) 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0