Unit 3

Useful Items

Unit 3: Categorical Logic

Lesson 4.0: Categories and Sets

Objectives

  • Define set, union, intersection, complement, and subset.
  • Compute operations on sets when given in list format.

Related Videos

  1. Preliminary Material on Sets

Required Exercises

  1. none

Supplemental Activities

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

Lesson 4.1 and 4.2: The Language of Categorical Statements

Objectives:

  • Identify the parts of categorical statements. 
  • Label categorical statements as: 
    • universal or particular
    • affirmative or negative
    • A, E, I or O

Related Videos

  1. (none at present)

Required Exercises

  1. Exercise 4.1 part I
  2. Exercise 4.2 part I

Supplemental Activities

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

Lesson 4.3: Venn Diagrams for Categorical Syllogisms

Objectives:

  • Generate a Venn diagram representing a categorical statement in standard form.

Related Videos

  1. Understanding Venn Diagrams
  2. Venn Diagrams and Categorical Statements

Required Exercises

  1. Exercise 4.3 part I

Supplemental Activities

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

Lesson 5.2: Venn Diagrams for Arguments

Objectives:

  • Use a Venn diagram to determine whether a categorical syllogism is valid.

Related Videos

  1. Syllogisms with Universals
  2. Syllogisms with Particulars

Required Exercises

  1. Exercise 5.2 part I

Supplemental Activities

  1. Under "Useful Items" on the right, I have posted a link to a syllogism generator created by the "Power of Logic" textbook and website, which you can access for free. It will generate a syllogism, and ask you to fill in a Venn diagram by clicking on its regions. Then it will check the work for you. Their Venn diagrams are upside down relative to ours, but you can still use it for practice.
Exercises Due: See Schedule

Lesson 4.7: Converting Ordinary Statements Into Standard Form

Objectives:

  • Restate ordinary statements as categorical statements in standard form. 

Related Videos

  1. Rewriting in Standard Form
  2. Rewriting in Standard Form Part I

Required Exercises

  1. See schedule

Supplemental Activities

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

Lesson 4.4 and 5.4: Logical Relationships Between Categorical Statements (Optional)

This section pertains to the extra credit portion of the test. Going through these materials should make it possible to get the extra credit points.

Objectives:

  • Translate a categorical statement into whichever of the following is equivalent: the converse, the obverse, or the contrapositive.

Related Videos

  1. (None at present)

Recommended Exercises

  1. See schedule

Supplemental Activities

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

Unit 3 Test

  • Book Sections Covered: 4.1, 4.2, 4.3, 4.7, 5.2, Extra Credit based on 4.4 and 5.4.
  • Identify the quantifier, subject, copula, and predicate in a categorical statement.
  • Identify the quantity and quality of a categorical statement.
  • Identify the letter associated with a categorical statement.
  • Draw a Venn diagram for a categorical statement.
  • Translate a statement expressed in natural terms as a statement into "standard form" for categorical statements.
  • Use a Venn diagram to determine whether a syllogism is valid.
  • Extra Credit: Reduce the number of terms in a categorical argument by using conversion, obversion, and/or contraposition. Then use a Venn Diagram to determine whether the resulting syllogism is valid.
Exercises Due: See Schedule