A truth table is a table used to establish the meaning of a logical connective as well as determining the validity of an argument. It is written as a two-dimensional array with n + 1 columns where n corresponds to the number of possible inputs. The last column, n + 1, is the column associated with the operation being performed. The number of rows in a truth table is dependent upon the type of statements given, either simple statements or compound statements. Truth tables are used in everything from binary logic to logic circuit tables in conjunction with Boolean operators.

During the late 1800s formal logic attempted to devise a complete, consistent formulation of mathematics. This formulation would be such that propositions could be formally stated and proved using a small number of symbols. Alfred North Whitehead's and Bertrand Russell's Principia Mathematica, published in 1925, showed that the problems with formal...