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# Logic II

## Exercise your rationality and learn the mathematical dialects of logic!

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.

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1. 1

### Introduction

Survey the logical languages in the course, and solve some interesting puzzles on the way.

1. #### Fallacies

Deduce which arguments are valid or invalid.

2. #### Knights, Knaves, and Logic

Practice some classic knights and knaves puzzles.

3. #### Knights and Formal Logic

Use a knight and knaves puzzle to learn the beginnings of advanced logic.

2. 2

### Syllogisms and Sets

Visual tools for laying out logical thinking and avoiding fallacies.

1. Included with

#### Euler and Venn Diagram Basics

Using diagrams to relate categories is an essential tool for approaching syllogisms.

2. Included with

#### All, Some, and None

What do the statements "all", "some", and "none" look like visualized with Venn diagrams?

3. Included with

#### Spot the Fallacies!

Try to tell logic from illogic.

4. Included with

#### The Square of Opposition

See how different syllogism statements are related to each other.

3. 3

### Arithmetic With Logic Gates

Build the functions of arithmetic using only logic gates.

1. Included with

#### Binary Refresher

Review the basics of binary.

2. Included with

#### Creating a Binary Comparator

When is one number larger than another?

3. Included with

#### Subtraction

Get into deeper complexity with binary subtraction.

4. Included with

#### Multiplication

Design the standard algorithm with logic circuits, then study an interesting shortcut.

4. 4

### Propositional Logic

Turn logic puzzles into logic symbols.

1. Included with

#### Introduction to Formal Logic

Learn the basic terminology of formal logic.

2. Included with

#### Formal De Morgan

Prove De Morgan's Laws with formal logic tools.

3. Included with

#### Using Implication

Apply implication to break open new laws of thought!

4. Included with

#### Rules of Substitution

Which rules of substitution are logically valid?

5. 5

### First-Order Logic

With a little extra logical power, describe the universe.

1. Included with

#### For All and There Exists

Practice using "all" and "some" formally and logically.

2. Included with

#### Formal Symbolization

Learn how to represent statements in first-order logic with formal notation.

3. Included with

#### Multiple Generality

Modify multiple logical variables rather than just one.

4. Included with