Module 7: Logic (Chapter 7)

What is logic? Logic is the study of reasoning, and it has applications in many fields, including philosophy, law, psychology, digital electronics, and computer science.

In law, constructing a well-reasoned, logical argument is extremely important. The main goal of arguments made by lawyers is to convince a judge and jury that their arguments are valid and well-supported by the facts of the case, so the case should be ruled in their favor. Think about Thurgood Marshall arguing for desegregation in front of the U.S. Supreme Court during the Brown v. Board of Education of Topeka lawsuit in 1954, or Ruth Bader Ginsburg arguing for equality in social security benefits for both men and women under the law during the mid-1970s. Both these great minds were known for the preparation and thoroughness of their logical legal arguments, which resulted in victories that advanced the causes they fought for. Thurgood Marshall and Ruth Bader Ginsburg would later become well respected justices on the U.S. Supreme Court themselves.

In this chapter, we will explore how to construct well-reasoned logical arguments using varying structures. Your ability to form and comprehend logical arguments is a valuable tool in many areas of life, whether you're planning a dinner date, negotiating the purchase of a new car, or persuading your boss that you deserve a raise.

Image Caption: Logic is key to a well-reasoned argument, in both math and law. (credit: modification of work "Lady Justicia holding sword and scale bronze figurine with judge hammer on wooden table" by Jernej Furman/Flickr, CC BY 2.0)

(Content & Image Source: Chapter 2 Introduction, Contemporary Mathematics, Donna Kirk, OpenStax, CC BY 4.0 License)

• Identify logical statements.
• Represent statements in symbolic form.
• Negate statements in words.
• Negate statements symbolically.
• Translate negations between words and symbols.
• Express statements with quantifiers of all, some, and none.
• Negate statements containing quantifiers of all, some, and none.

• Translate compound statements into symbolic form.
• Translate compound statements in symbolic form with parentheses into words.
• Apply the dominance of connectives.

• Interpret and apply negations, conjunctions, and disjunctions.
• Construct a truth table using negations, conjunctions, and disjunctions.
• Construct a truth table for a compound statement and interpret its validity.

1. Read the Module 7 Introduction (see above)
   
2. Read Sections 7.1 - 7.7 of Chapter 7: Logic in Finite Mathematics (links to each Section provided below)
3. Watch the Videos provided in the Video Lessons pages for each Section (links provided below)
   
4. Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
   
5. Complete the MyOpenMath Quiz for Chapter 7 (link provided below) - This is graded!
6. Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
7. Post in the Chapter 7 Q&A Discussion Forum - link provided below.

Module Pressbooks Resources and Activities