We won't have the tools we need for a proper quiz until we can make a basic proof, so we will spend today and Tuesday next week developing what we need to do that.

Today we will complete Section 1.3: Rules of Logic, reading the section and working the exercises (especially working the exercises!).

The plan is to have the first quiz next Friday.

Let's divide up the Additional Exercises for the presentation of solutions in class next Wednesday. There are 17 exercises, so we can have each of you choose one you would like to present. I'll record which ones you choose in this table:

Arya

Rules of Logic Additional Exercises
Exercise	Presenter	Exercise	Presenter	Exercise	Presenter
1	Mason	7	Nathan	13	Dimitri
2	Delanie	8	Sean	14
3	Robbie	9	Stephen	15
4	Giselle	10	Evan	16
5	Antoan	11		17
6	Waleed	12

Your evaluation for this week will be based on your notes in your git repo. Be sure to include all definitions and theorems in your notes. I will look over your repos on Monday, so this assignment is due Sunday, February 15 at 11:59 pm.

We have a short class today, and a few students may have a challenge getting here since buses from their school aren't running, so we will use class time for those that are here in a way that won't negatively impact them.

We'll begin by discussing any questions you have from the exercises from Section 1.1: Mathematical Statements. I'll share my notes from this section, and use them for a brief discussion of how to take notes on this material.

Run:

ttg_cli.py "['P', 'Q']" -p "['P => Q', 'Q => P', '~Q => ~P', '~P => ~Q']" -i False

in your terminal. What do you observe?

Take notes on Section 1.2: Implications in your git repo. Complete the Reading Questions, Practice Problems, and three Additional Exercises at the end of the section. Come to our next class prepared to discuss the section.

Your next evaluation will be of your notes for this and the following section which I'll make over the weekend. We will have our first quiz next week after we complete Section 1.3: Rules of Logic.

Today in class we will discuss Section 1.1: Mathematical Statements in our text. Since it will be so useful to us as we explore logical statements, we will start by installing truth-table-generator and learning how to use it to investigate the mathematical statements presented in the section.

Here are the two steps needed to get truth-table-generator working on your school Macbook:

1. Run: python3 -m pip install truth-table-generator
2. In your .zshrc file add the path to the installed library. To find it, first run:

   % find / -iname ttg_cli.py 2>/dev/null
   

   and look at the matches you get. Today I tried this on the Macbook Pro I have running Sequoia 15.7.3, and my library path is:

   /Library/Frameworks/Python.framework/Version/3.13/bin
   

   We'll use this as a teachable moment to learn more about environment variables and managing computer systems. Add the path to your environment by editing your .zshrc file and adding:

   export PATH=$PATH:[the path to your ttg_cli.py]
   

   I'll help you with this in class.

That done, we will work through the following examples together.

1. ttg_cli.py "['p']"
2. ttg_cli.py "['p', 'q']"
3. ttg_cli.py "['p', 'q', 'r']"
4. ttg_cli.py "['p']" -i False
5. ttg_cli.py "['p', 'q']" -p "['~(p and q)', 'p or ~q']" -i False
6. ttg_cli.py "['p', 'q', 'r', 's'] -i False"
7. ttg_cli.py "['p', 'q']" -p "['p and q', 'p or q', 'p => q']" -i False

Find a statement logically equivalent (i.e. having the same truth table) to p => q using or and ~ operators.

Given the following propositional variables:

• p: Troll 1 is a knave.
• q: There are exactly two knights.
• r: Troll 1 is lying.
• s: All 3 Trolls are knaves.

use truth-table-generator to explore the Investigate! activity in the Section Preview of Section 1.1 Mathematical Statements. See if you can determine which Trolls are knaves and which are knights.

Take notes on section 1.1, and learn the following vocabularly and be prepared to use it correctly:

• premise
• conclusion
• argument
• theorem
• proposition
• proof
• statement
• quantifier
• predicate
• logical connective
• binary connective
• unary connective
• truth value
• propositional variables
• conjunction
• disjunction
• implication
• conditional
• biconditional
• negation
• truth conditions

Complete the Reading Questions, Practice Problems, and three Additional Exercises at the end of the section. Come to our next class prepared to discuss these exercises.