Unit 2

Useful Items

Unit 2: Propositional Logic

Lesson 6.0: Introducing Symbolic Logic

Objectives

  • Define the concept of a formal language.
  • Axiomatize the syntax of propositional logic. 
  • Distinguish strings of symbols that are sentences of propositional logic from those that are not. 
  • Identify the main operator of a given sentence of propositional logic.

Related Videos

  1. Lesson 6.0.1: Formal Languages
  2. Lesson 6.0.1: Syntax for propositional logic, Part I
  3. Lesson 6.0.2: Syntax for propositional logic, Part II

Required Exercises

  1. Exercise 6.2 Part I

Supplemental Activities

  1. I'll post ideas here as I come up with them.
Exercises Due: See Schedule

Lesson 6.1 and 6.2: Modelling Language, and Truth Functions

Objectives:

  • Define truth functional significance for each operator of propositional logic.
  • Establish modeling relationships between sentences of propositional logic and ordinary statements. 
  • Produce representations of English sentences using propositional logic. 
  • Compute the truth value of a given sentence of propositional logic on an assignment of truth values to the simple sentences involved. 

Related Videos

  1. Lesson 6.1.0: Simple Statements, Negations, and Conjunctions 
  2. Lesson 6.1.1: Disjunctions 
  3. Lesson 6.1.2: Conditional Statements
  4. Lesson 6.1.3: Biconditional Statements

Required Exercises

  1. Exercises 6.1 part I and 6.2 part III

Supplemental Activities

  1. I'll post ideas here as I come up with them.
Exercises Due: See Schedule

Lesson 6.3: Completing and Applying Truth Tables

Objectives:

  • Generate all possible semantic assignments for a given sentence or pair of sentences. 
  • Complete a truth table by computing the truth value of a sentence or pair of sentences for each possible semantic assignment.
  • Analyze the truth table to determine whether a sentence is tautologous, self-contradictory, or contingent.

Related Videos

  1. Lesson 6.3.1: Tautologous, Self-Contradictory, or Contingent
  2. Lesson 6.3.2: Sentence Pairs

Required Exercises

  1. Exercise 6.3 parts I. Show all work.
  2. Exercise 6.3 part II. Show all work.

Supplemental Activities

  1. Watch this video on how to do truth tables quickly and easily in MS Word.
  2. I'll post more ideas here as I come up with them.
Exercises Due: See Schedule

Lesson 6.4: Using Truth Tables to Determine Validity

Objectives:

  • Use a truth table to determine whether an argument is valid. 

Related Videos

  1. Read section 6.4 of the textbook. 
  2. Watch the video lectures below.

Required Exercises

  1. Exercise 6.4 part II. Show all work.

Supplemental Activities

  1. I'll post ideas here as I come up with them.
Exercises Due: See Schedule

Lesson 7.1 and 7.2: Inference Rules and the Rules of Implication

Objectives:

  • Derive a conclusion from a set of given sentences using the rules of implication.

Related Videos

  1. Lesson 7.0: How Inference Rules Work and Modus Ponens
  2. Lesson 7.1 and 7.2: Rules of Implication

Required Exercises

  1. Complete the following exercises and submit them all as one assignment, worth 20 points.
  • 7.1 part I #1-8
  • 7.1 part II #1-8
  • 7.2 part I #1-8
  • 7.2 part II #1-8

Supplemental Activities

  1. I'll post ideas here as I come up with them.
Exercises Due: See Schedule

Lesson 7.3 and 7.4: Rules of Replacement

Objectives:

  • Derive a conclusion from a set of given sentences using the rules of replacement, together with the rules of implication.

Related Videos

  1. Lesson 7.3: Rules of Replacement
  2. Lesson 7.4: Rules of Replacement II Plus Examples

Required Exercises

  1. Complete the following exercises and submit them as one assignment, worth 30 points.

    • 7.3 part I #1-8
    • 7.3 part II #1-8
    • 7.3 part III #1-8
    • 7.4 part I #1-8
    • 7.4 part II #1-8
    • 7.4 part III #1-10

Supplemental Activities

  1. I'll post ideas here as I come up with them.
Exercises Due: See Schedule

Unit 2 Test

The following is a list of tasks you will be asked to perform on the test. You should use this sheet as a checklist for studying. You should also use it to keep track of test material as it is covered in class.

Topic One: Symbolization and Truth Tables

  • Symbolize an English sentence in propositional logic.
  • Construct a truth table for a symbolized sentence.
  • Determine the truth value of a symbolized compound sentence, given the truth values of its simplest constituents.
  • Use a truth table to determine whether a group of symbolized sentences is consistent, inconsistent, equivalent, or contradictory, or some combination of the above.
  • Use a truth table to determine whether an argument is valid.

Topic Two: Proof System

  • Identify the inference rule that licenses a given conclusion.
  • Produce the conclusion licensed by an inference rule and a set of premises.
  • (Extra Credit) Prove a conclusion from a set of symbolized assumptions, naming the rule and the premises that justify each conclusion, from the list provided.
Test Date: See Schedule