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# Logic II

via Brilliant

### 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.

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