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Propositional Logic Fundamentals

Mathematics

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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

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Propositional Logic course, This course delves into the fundamentals of Propositional Logic, exploring its rules and applications in logical reasoning and problem-solving.

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