Discrete Mathematics

Introduction to Discrete Mathematics
Motivation & Introduction to Propositional Logic
Propositional Logic, Propositional Variables & Compound Propositions
Logical Operators − Negation, Conjunction & Disjunction
Logical Operators − Exclusive OR
Logical Operators − Implication (Part 1)
Logical Operators − Implication (Part 2)
Logical Operators − Implication (Part 3)
Converse, Contrapositive and Inverse
Logical Operators − Biconditional Operator
Propositional Logic − Precedence of Logical Operators
Translating Sentences into Logical Expressions
Propositional Logic − Puzzle 1
Propositional Logic − Puzzle 2
Propositional Logic (Solved Problem 1)
Tautology, Contradiction, Contingency & Satisfiability
Propositional Logic − Logical Equivalences
Propositional Logic (Solved Problem 2)
Propositional Logic (Solved Problem 3)
Propositional Logic (Solved Problem 4)
Propositional Logic (Solved Problem 5)
Propositional Logic (Solved Problem 6)
Propositional Logic (Solved Problem 7)
Rules of Inference - Basic Terminology
Rules of Inference - Definition & Types of Inference Rules
Arguments Building Using Rules of Inference (Part 1)
Arguments Building Using Rules of Inference (Part 2)
Checking The Validity of An Argument (Shortcut Method)
Rules of Inference in Propositional Logic (Solved Problem 1)
Rules of Inference in Propositional Logic (Solved Problem 2)
The Limitation of Propositional Logic
Introduction to First Order Logic
Finding The Truth Values of Predicates (Examples)
Quantifiers
Universal Quantifiers
Universal Quantifiers - Counter Examples
Expressing Quantifications in English
Existential Quantifiers
Existential Quantifiers - Examples
Quantifiers with Restricted Domain
Logical Equivalences Involving Predicates & Quantifiers (Part 1)
Logical Equivalences Involving Predicates & Quantifiers (Part 2)
Negating the Quantified Expressions (Part 1)
Negating the Quantified Expressions (Part 2)
Negating the Quantified Expressions (Examples)
Translating English Sentences to Logical Expressions
First Order Logic (Solved Problems) - Part 1
First Order Logic (Solved Problems) - Part 2
First Order Logic (Solved Problems) - Part 3
First Order Logic (Solved Problems) - Part 4
First Order Logic (Solved Problems) - Part 5
Introduction to Nested Quantifiers
Nested Quantifiers (Solved Example 1)
Nested Quantifiers (Solved Example 2)
Nested Quantifiers (Solved Example 3)
Nested Quantifiers (Translating English Statements) - Example 1
Nested Quantifiers (Translating English Statements) - Example 2
Nested Quantifiers (Translating English Statements) - Example 3
Nested Quantifiers (Translating English Statements) - Example 4
Nested Quantifiers (Translating English Statements) - Example 5
Negating the Nested Quantifiers
Negating the Nested Quantifiers (Example 2)
Negating the Nested Quantifiers (Example 3)
The Resolution Principle (Preliminaries)
The Resolution Principle (Proof of Theorem)
The Resolution Principle (Proving if an Argument is Valid)
The Resolution Principle (Solved Problems)
Fallacies
Rules of Inference for Quantified Statements (Part 1)
Rules of Inference for Quantified Statements (Part 2)
Universal Modus Ponens Rule
Universal Modus Tollens Rule
Set Theory (Basics of Sets)
Set Representation
Inclusion and Equality
Inclusion vs. Membership
Inclusion vs. Membership (Solved Problem)
Types of Sets - Universal, Null, and Singleton
Null Set (Solved Problem)
Non-Empty Set (Important Theorem)
Power Set
Power Set (Solved Problems)
Power Set (GATE Problem 1)
Power Set (GATE Problem 2)
Cardinality of Sets
Cartesian Product
Cartesian Product (Solved Problems)
Set Operations (Intersection & Union with Venn Diagram)
Set Difference and Set Complement
Set Operations (Solved Problems)
Set Identities (Part 1)
Set Identities (Part 2)
Set Identities (Part 3)
Set Operations (Solved Problem 1)
Set Operations (Solved Problem 2)
Symmetric Difference
Set Operations (GATE Problems)
Set Operations (GATE and TIFR Problem)
Introduction to Relations
Types of Relations (Part 1)
Types of Relations (Part 2)
Types of Relations (Solved Problem)
Types of Relations (GATE Problems) - Set 1
Types of Relations (GATE Problems) - Set 2
Operations on Relations
Composition of Relations
Composition of Relation with Itself
Representation of Relations
Closure of Relations – Part 1
Closure of Relations – Part 2
Closure of Relations (Solved Problems) - Set 1
Warshall's Algorithm (Finding the Transitive Closure)
Closure of Relations (Solved Problems) - Set 2
Closure of Relations - GATE Problem
Equivalence Relation
Equivalence Relation (Solved Problems)
Equivalence Relation (GATE Problems) - Set 1
Equivalence Relation (GATE Problems) - Set 2
Equivalence Relation (GATE Problem)
Equivalence Classes
Congruence Modulo m
Modulus of Negative Numbers
Equivalence Classes and Partitions
Equivalence Classes and Partitions (Solved Problems)
Introduction to Partial Ordering
Partial Orderings (Solved Problems) - Set 1
Partial Orderings (Solved Problems) - Set 2
Hasse Diagram
Hasse Diagram (Solved Problems) - Set 1
Hasse Diagram (Solved Problems) - Set 2
Poset (Minimal and Maximal Elements)
Poset (Least and Greatest Elements)
Poset (Lower and Upper Bounds)
Poset (Least Upper Bound and Greatest Lower Bound)
Hasse Diagram (Solved Problems) - Set 3
Symbols for Partial Order
Meet Semilattice
Join Semilattice
Lattice
Lattice (GATE Problems) - Set 1
Complete and Bounded Lattice
Lattice (Complement of an Element)
Lattice (GATE Problems) - Set 2
Complemented Lattice
Distributive Lattice
Functions | Chapter-7 | Discrete Mathematics | nesoacademy.org
Counting | Chapter-8 | Discrete Mathematics | nesoacademy.org
Permutations & Combinations | Chapter-9 | Discrete Mathematics | nesoacademy.org