Week 1

Chapters (Discrete Mathematics and Its Applications):

• 1.1 Propositional Logic
  • 1.1.1 Introduction
  • 1.1.2 Propositions
  • 1.1.3 Conditional Statements
  • 1.1.4 Truth Tables of Compound Propositions
  • 1.1.5 Precedence of Logical Operators
  • 1.1.6 Logic and Bit Operations
• 1.3 Propositional Equivalences
  • 1.3.1 Introduction
  • 1.3.2 Logical Equivalences
  • 1.3.3 Using De Morgan’s Laws
  • 1.3.4 Constructing New Logical Equivalences
• 1.4 Predicates and Quantifiers
  • 1.4.1 Introduction
  • 1.4.2 Predicates
  • 1.4.3 Quantifiers
  • 1.4.4 Quantifiers Over Finite Domains
  • 1.4.5 Quantifiers with Restricted Domains
  • 1.4.6 Precedence of Quantifiers
  • 1.4.7 Binding Variables
  • 1.4.8 Logical Equivalences Involving Quantifiers
  • 1.4.9 Negating Quantified Expressions

Videos:

• Introduction
• Propositional Logic
  • 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
• Predicates
  • Introduction to First Order Logic
• Quantifiers
  • 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

Exercises:

• Propositional Logic − Puzzle 1
• Propositional Logic − Puzzle 2
• Propositional Logic (Solved Problem 1)

• Finding The Truth Values of Predicates (Examples)

• Negating the Quantified Expressions (Examples)

• 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