Category archives: Propositional Logic

Induction Proofs: Generalized Rules of De Morgan and Distribution SUMMARYThis class addresses the topic of induction proofs in mathematics and propositional logic. The two types of existing proofs are explained: internal or deductive proofs, which are based on the rules of logic, and external or metamathematical proofs, which are necessary…

Induction on the Complexity of Formulas SUMMARYIn this class, you will learn about a variant of mathematical induction, known as “induction on the complexity of expressions,” which is very useful for proving properties in propositional logic. Through a simple example, the substitution theorem, you will see how this technique is…

Normal Forms and Their Properties SUMMARYPropositional logic is a fundamental tool in mathematics and computer science. In this class, an interesting and useful result related to normal forms will be presented. To achieve this, the concepts of literal, conjunctive normal form (CNF), and disjunctive normal form (DNF) will be defined….

Normal Form Algorithm and Applications SUMMARYIn this class, we will review the DNF/CNF algorithm, which will allow us to find, from any expression in propositional logic, its equivalent expression in conjunctive or disjunctive normal form. We will begin by explaining the three steps that make up this algorithm, which consist…