Udemy, Coursera, 2U/edX Face Lawsuits Over Meta Pixel Use

Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Brilliant

Logic II

via Brilliant

Go to class Write review

Overview

Continue your adventures in logic with puzzles involving Venn diagrams and syllogisms, propositional logic, and first-order logic.

By the end of this course you'll have explored the deep foundations of truth as well as applied logic to AI expert systems and linguistic analysis.

Syllabus

  • Introduction: Survey the logical languages in the course, and solve some interesting puzzles on the way.
    • Fallacies: Deduce which arguments are valid or invalid.
    • Knights, Knaves, and Logic: Practice some classic knights and knaves puzzles.
    • Knights and Formal Logic: Use a knight and knaves puzzle to learn the beginnings of advanced logic.
  • Syllogisms and Sets: Visual tools for laying out logical thinking and avoiding fallacies.
    • Euler and Venn Diagram Basics: Using diagrams to relate categories is an essential tool for approaching syllogisms.
    • All, Some, and None: What do the statements "all", "some", and "none" look like visualized with Venn diagrams?
    • Spot the Fallacies!: Try to tell logic from illogic.
    • The Square of Opposition: See how different syllogism statements are related to each other.
    • And, Or, and Not: Use Venn diagrams to think through statements that combine "and", "or", and "not".
    • De Morgan's Laws: Apply your intuition to discover two fundamental laws of logic.
  • Logic Machines: Turn logic into arithmetic machines.
    • Truth Tables: Diagram out the meanings of each logical operator.
    • Basic Logic Gates: How do AND, OR, and NOT gates work?
    • Combinations: Combine gates together to make complex circuits.
    • Fredkin Gates: Take a peek at a gate used in biological and quantum computing.
    • Binary Numbers and Addition: How does computer arithmetic work?
    • Creating a Mechanical Adder: Use what you've learned about logic gates to create a circuit that adds numbers.
  • Arithmetic With Logic Gates: Build the functions of arithmetic using only logic gates.
    • Binary Refresher: Review the basics of binary.
    • Creating a Binary Comparator: When is one number larger than another?
    • Subtraction: Get into deeper complexity with binary subtraction.
    • Multiplication: Design the standard algorithm with logic circuits, then study an interesting shortcut.
    • Division: Finish the quadrilogy of arithmetic with one last design.
  • Propositional Logic: Turn logic puzzles into logic symbols.
    • Introduction to Formal Logic: Learn the basic terminology of formal logic.
    • Formal De Morgan: Prove De Morgan's Laws with formal logic tools.
    • Using Implication: Apply implication to break open new laws of thought!
    • Rules of Substitution: Which rules of substitution are logically valid?
    • Knights and Knaves Redux: Learn how to solve challenging knights and knaves puzzles using formal logic.
  • First-Order Logic: With a little extra logical power, describe the universe.
    • For All and There Exists: Practice using "all" and "some" formally and logically.
    • Formal Symbolization: Learn how to represent statements in first-order logic with formal notation.
    • Multiple Generality: Modify multiple logical variables rather than just one.
    • Duals and Prenex: Transform first-order logic statements using duals and learn about prenex form.
    • Quantifiers and Proof (I): Learn how to introduce and eliminate existential quantifiers.
    • Quantifiers and Proof (II): Derive complex proofs with universal generalizations and existential instantiations.
    • Functions and Identity: Apply logic to functions and arithmetic.

Reviews

Start your review of Logic II

Go to class

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.