Videos

Introduction to Sets

More about Sets

Set Operations

Symmetric Difference Examples

Set Identities

Proving Set Identities

Intro to Propositional Logic

Statement Identification and Translation Examples

Truth Tables

Truth Tables Examples

NOT, AND, OR, and XOR

Conditional Statements

Conditional Examples

Biconditional Statements

Proofs with Truth Tables

Logical Equivalence

Tautologies, Contradictions, and Contingencies

Propositional Satisfiability

Negating Quantifiers and Translation Examples

Predicates and Quantifiers

Checking the Validity of an Argument

Analyzing an Argument for Validity

Direct Proof

Direct Proof - Practice

Direct Proof in Arabic

Direct Proof - Step-by-step guide

Proof by Contrapositive

Proof by Contrapositive

Proof Methods and Strategy

• Covers Proof by Cases, WLOG, Existence and Uniqueness Proofs

Proof by Cases

Divisibility

Divisibility Examples

Modular Arithmetic

Congruency Proof Examples

What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence

Proof Involving Sets

Proof Involving Sets

Set Operations

Set Operations

Cartesian Products

Cartesian Product Proofs

Proof by Contradiction

Contradiction

Proof by Contradiction

Proofs of Existence And Uniqueness

Proofs of Existence And Uniqueness

Unique Quantifier Examples

Well-Ordering Principle

Principle Of Mathematical Induction | Visualization

Why Does Mathematical Induction Work?

Strong Induction

Equivalence Relations - Reflexive, Symmetric, and Transitive

Equivalence Classes

Composition of Functions

Composite Functions