Motivations and background
Boolean algebra

Boolean algebra is at the heart of mathematical logic, set theory, information theory, algorithms and their complexity.

• Predicate calculus

  Propositional calculus ("the Laws of Thought") provides a language and rules for formalizing elementary intuitive reasoning. A proposition is a formula whose truth value (true or false) can be evaluated from the truth values given to the input variables x₁, x₂,..., x_n.

  Thus, p (x₁, x₂) := (x₁ and x₂) or (not x₁ and not x₂) is true if x₁ = x₂ = true, or if x₁ = x₂ = false; it is false otherwise. The proposition q (x₁, x₂) := not (x₁...