Explore a comprehensive tutorial on discrete mathematics covering essential topics for GATE, UGC NET, PSUs, and college/university exams. Delve into set theory, relations, group theory, and functions through detailed explanations and examples. Begin with an introduction to set theory, including subsets and power sets, before progressing to various types of relations such as reflexive, symmetric, and transitive. Examine algebraic structures, semigroups, monoids, and groups, including Abelian groups. Conclude with an in-depth look at functions, exploring injection, surjection, and bijection. Master key concepts and formulas to excel in discrete mathematics examinations and applications.