An Introduction to Proofs with Set Theory

"An Introduction to Proofs with Set Theory" is a textbook designed as an introduction to mathematical proofs for students. It is based on the lecture notes of a course that focuses on the topics of set theory to enhance the understanding of proofs. The book begins with an introduction that covers fundamental concepts and background materials that may be new to many students. It guides readers through the basics of logic, including Boolean logic, propositions and predicates, as well as logical operations and rules of argumentation. Additionally, various types of mathematical proofs, naive set theory, mathematical induction, and recursive relationships are discussed. The book also provides an overview of functions, including injective, surjective, and bijective functions, as well as basic properties of integers and an introduction to combinatorics. It is a comprehensive work that addresses both theoretical and practical aspects of set theory and mathematical proof techniques.