Week 3

Chapters (Discrete Mathematics and Its Applications):

• 1.7 Introduction to Proofs
  • 1.7.1 Introduction
  • 1.7.2 Some Terminology
  • 1.7.3 Understanding How Theorems Are Stated
  • 1.7.4 Methods of Proving Theorems
  • 1.7.5 Direct Proofs
  • 1.7.6 Proof by Contraposition
  • 1.7.7 Proofs by Contradiction
  • 1.7.8 Mistakes in Proofs
• 5.1 Mathematical Induction

Videos:

• Nested Quantifiers
  • Introduction to Nested Quantifiers
  • Negating the Nested Quantifiers
• Rules of Inference for Quantified Statements
  • Part 1
  • Part 2
• Universal Modus Ponens Rule
• Universal Modus Tollens Rule
• Proof by Contradiction
• Proof by Contrapositive
• Proof by Induction
  • Intro to Mathematical Induction
  • Induction Proofs Involving Inequalities

Exercises:

• 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 (Example 2)
• Negating the Nested Quantifiers (Example 3)