In the language of mathematics and logic there are essentially two types of statements. There are basic propositions (abbreviated here by lower-case, italicized letters, e.g., p, q, etc.), like "the triangle ABC is equilateral," or "the integer a is odd." Then there are complex propositions which are constructed from the basic propositions by connectives: conjunction ("p and q"), disjunction ("p or q"), negation (not-p), and implication ("if p then q). These connectives are truth-functional, meaning that the truth-value of the complex sentence is a function of the truth-values of the connected basic sentences. Each connective can be considered a truth function.

Truth functions are formally defined. Like any other function, a truth function is associated with two sets, a domain set and a range set. A function is a rule that associates each unique object in the first set with exactly one object in the...