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.
Overview
Syllabus
L-0: Discrete Mathematics Syllabus for GATE, UGC NET, PSUs & COLLEGE/UNIVERSITY Exams.
L-1.1: Introduction to Set Theory | Set, Subset, Proper Subset.
L-1.2: Power Set | Set Theory & Algebra.
L-2.1: Relation in Set Theory with examples.
L-2.2: Reflexive Relation with examples | Discrete Mathematics.
L-2.3: How Many Reflexive Relations Possible | Discrete Mathematics Formulas.
L-2.4: Irreflexive Relation with examples | Discrete Mathematics.
L-2.5: Symmetric Relation with examples | Discrete Maths.
Antisymmetric Relation with examples | Discrete Maths.
Asymmetric vs Antisymmetric Relation with examples.
Transitive Relation with examples.
Equivalence Relation in Discrete Mathematics with examples.
Partial Order Relation | POSET in Discrete Mathematics.
Totally Ordered Set in Discrete Mathematics.
Comparison of All Relations | Reflexive,Irreflexive,Transitive, Symmetric,Antisymmetric, Asymmetric.
Introduction to Group Theory | Discrete Mathematics.
Algebraic structure in Discrete Mathematics.
Semigroup in Group Theory | Discrete Mathematics.
Monoid in Discrete Mathematics | Group Theory.
Group in Discrete Mathematics with examples in Hindi.
Abelian Group in Discrete Mathematics with examples.
Function in Discrete Mathematics.
How many Functions Possible | Counting Functions | Discrete Mathematics.
One to One Function (Injection) | Injective Function.
ONTO Function(Surjection) | Surjective Function | Discrete Mathematics.
Bijective Function (Bijection) | Discrete mathematics.
Taught by
Gate Smashers
