The Empty Set & Vacuous Truth

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• ✓1Intro to Discrete Math - Welcome to the Course!
• ✓2Intro to Sets | Examples, Notation & Properties
• ✓3Set-Roster vs Set-Builder notation
• ✓4The Empty Set & Vacuous Truth
• ✓5Cartesian Product of Two Sets A x B
• ✓6Relations between two sets | Definition + First Examples
• ✓7The intuitive idea of a function
• ✓8Formal Definition of a Function using the Cartesian Product
• ✓9Example: Is this relation a function?
• ✓10Intro to Logical Statements
• ✓11Intro to Truth Tables | Negation, Conjunction, and Disjunction
• ✓12Truth Table Example: ~p V ~q
• ✓13Logical Equivalence of Two Statements
• ✓14Tautologies and Contradictions
• ✓153 Ways to Show a Logical Equivalence | Ex: DeMorgan's Laws
• ✓16Conditional Statements: if p then q
• ✓17Vacuously True Statements
• ✓18Negating a Conditional Statement
• ✓19Contrapositive of a Conditional Statement
• ✓20The converse and inverse of a conditional statement
• ✓21Biconditional Statements | "if and only if"
• ✓22Logical Arguments - Modus Ponens & Modus Tollens
• ✓23Logical Argument Forms: Generalizations, Specialization, Contradiction
• ✓24Analyzing an argument for validity
• ✓25Predicates and their Truth Sets
• ✓26Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists"
• ✓27Negating Universal and Existential Quantifiers
• ✓28Negating Logical Statements with Multiple Quantifiers
• ✓29Universal Conditionals P(x) implies Q(x)
• ✓30Necessary and Sufficient Conditions
• ✓31Formal Definitions in Math | Ex: Even & Odd Integers
• ✓32How to Prove Math Theorems | 1st Ex: Even + Odd = Odd
• ✓33Step-By-Step Guide to Proofs | Ex: product of two evens is even
• ✓34Rational Numbers | Definition + First Proof
• ✓35Proving that divisibility is transitive
• ✓36Disproving implications with Counterexamples
• ✓37Proof by Division Into Cases
• ✓38Proof by Contradiction | Method & First Example
• ✓39Proof by Contrapositive | Method & First Example
• ✓40Quotient-Remainder Theorem and Modular Arithmetic
• ✓41Proof: There are infinitely many primes numbers
• ✓42Introduction to sequences
• ✓43The formal definition of a sequence.
• ✓44The sum and product of finite sequences
• ✓45Intro to Mathematical Induction
• ✓46Induction Proofs Involving Inequalities.
• ✓47Strong Induction // Intro and Full Example
• ✓48Recursive Sequences
• ✓49The Miraculous Fibonacci Sequence
• ✓50Prove A is a subset of B with the ELEMENT METHOD
• ✓51Proving equalities of sets using the element method
• ✓52The union of two sets
• ✓53The Intersection of Two Sets
• ✓54Universes and Complements in Set Theory
• ✓55Using the Element Method to prove a Set Containment w/ Modus Tollens
• ✓56Power Sets and the Cardinality of the Continuum
• ✓57Relations and their Inverses
• ✓58Reflexive, Symmetric, and Transitive Relations on a Set
• ✓59Equivalence Relations - Reflexive, Symmetric, and Transitive
• ✓60You need to check EVERY spot for reflexivity, symmetry, and transitivity
• ✓61Introduction to probability // Events, Sample Space, Formula, Independence
• ✓62Example: Computing Probabilities using P(E)=N(E)/N(S)
• ✓63What is the probability of guessing a 4 digit pin code?
• ✓64Counting with Triple Intersections // Example & Formula
• ✓65Permutations: How many ways to rearrange the letters in a word?
• ✓66The summation rule for disjoint unions
• ✓67Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B)
• ✓68Combinations Formula: Counting the number of ways to choose r items from n items.
• ✓69How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example
• ✓70Counting and Probability Walkthrough
• ✓71Intro to Conditional Probability
• ✓72Two Conditional Probability Examples (what's the difference???)
• ✓73Conditional Probability With Tables | Chance of an Orange M&M???
• ✓74Bayes' Theorem - The Simplest Case
• ✓75Bayes' Theorem Example: Surprising False Positives
• ✓76Bayes' Theorem - Example: A disjoint union
• ✓77IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability
• ✓78Intro to Markov Chains & Transition Diagrams
• ✓79Markov Chains & Transition Matrices
• ✓80Intro to Linear Programming
• ✓81Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg
• ✓82Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph
• ✓83Degree of Vertices | Definition, Theorem & Example | Graph Theory
• ✓84Euler Paths & the 7 Bridges of Konigsberg | Graph Theory
• ✓85The End of Discrete Math - Congrats! Some final thoughts...

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