Mathematical Logic : Course and exercises with solutions

Abstract

Logic is the first formalization of mathematical language and reasoning. It has been developed from the end of the 19th century, little by little, by a cohort of brilliant mathematicians and philosophers. Currently, in conjunction with the tremendous development in computer science, mathematical logic continues to be an active area of research, and made significant contributions in various fields such as: algorithm design, programming language theory, databases, artificial intelligence, logic gates, digital circuits, philosophy, linguistics, legal reasoning, etc. The aim of this course is to study in detail the foundations of mathematical logic. To give students sufficient training, the course is divided into 5 chapters as follows: In chapter 1, we begin by explaining the different concepts of mathematical language. In chapter 2, we study the different types of mathematical proofs, and provide illustrative examples of each one. In chapter 3, we present a comprehensive study of set theory, which is a fundamental focus for every mathematician. Chapter 4 and 5, is dedicated to propositional calculus and predicate calculus, respectively. Which are represent a fundamental systems in mathematical logic.