Set Theory, Relations, and Functions: Comprehensive Study Notes

These notes provide an in-depth exploration of key concepts in discrete mathematics, focusing on set theory, relations, and functions. The document includes definitions, theorems, and examples that explain the following topics: 1. Set Theory: Fundamental definitions of sets, subsets, power sets, and universal sets, with explanations on set operations like union, intersection, and difference. The notes also cover advanced topics like Cartesian products and Venn diagrams. 2. Relations: Definitions of different types of relations, such as reflexive, symmetric, transitive, and equivalence relations. Properties and examples of functions are included to demonstrate how relations between elements of sets can be described mathematically. 3. Functions: Detailed breakdown of types of functions, including injective (one-to-one), surjective (onto), and bijective functions. Examples illustrate function composition and inverse functions, with practical applications in mathematical problem-solving. These notes are more than sufficient to better understand the topics from basics and prepare for your exams!