Unit 5: Venn Diagrams In addition to using predicate logic, the limitations of sentential logic can also be overcome by using Venn diagrams to illustrate statements and arguments. Statements that include general words like “some,” or “few,” as well as absolute words like “every,” “all,” and so on, lend themselves to being represented on paper as circles that may or may not overlap. Venn diagrams are especially helpful when dealing with the logical arguments called syllogisms. Syllogisms are a special type of three-step argument with two premises and a conclusion, which involve “quantifying” terms. In this unit we will learn the basic principles of Venn diagrams, how to use them to represent statements, and how to use them to evaluate arguments.
Unit 5 Time Advisory
This unit should take you approximately 6.5 hours.
☐ Subunit 5.1: 3 hours
☐ Subunit 5.2: 3.5 hours
Unit5 Learning Outcomes
Upon successful completion of this unit, you will be able to:
- describe what a Venn diagram is;
- describe and illustrate what a class is;
- apply Venn diagrams to represent and reason about relationships
among classes;
- evaluate the validity of arguments using Venn diagrams;
- evaluate arguments for conditional validity using Venn diagrams; and
- describe and illustrate the limitations of Venn diagrams as
assessment tools.
5.1 Introduction to Venn Diagrams
5.1.1 Venn Diagrams as Illustrations of Sets or Classes
- Reading: University of Hong Kong’s Critical Thinking Web: Joe Lau
and Jonathan Chan’s Venn Diagrams: “Introduction and Tutorial
V01”
Links: University of Hong Kong’s Critical Thinking Web: Joe Lau and
Jonathan Chan’s Venn Diagrams:
“Introduction and Tutorial
V01” (HTML)
Instructions: Read these two tutorials for an introduction to Venn
diagrams. In Venn diagrams, circles represent sets or classes. These
tutorials demonstrate how to use shading and overlapping to
illustrate empty sets, as well as relations of all, every, and
nothing.
Reading these tutorials should take approximately 1 hour.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/).
5.1.2 More Complicated Venn Diagrams - Reading: University of Hong Kong’s Critical Thinking Web: Joe Lau and Jonathan Chan’s Venn Diagrams: “Tutorial V03” Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and Jonathan Chan’s Venn Diagrams: “Tutorial V03” (HTML)
Instructions: Read the tutorial, practice using the flash
animations, and complete all of the exercises on the page. Once you
have answered each question, check the [“Tutorial V03 Answer
Key”](https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2014/02/PHIL102-Subunit5.1.2-TutorialV03-FINAL.pdf)
(PDF).
Working with Venn diagrams that involve three circles is almost
exactly the same as working with ones that involve two circles. The
only difference is that there are now eight distinct regions, each
with a specific logical meaning.
Reading this tutorial and completing the exercises should take
approximately 30 minutes.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/venn/tute3.php).
5.1.3 Illustrating Existence with Venn Diagrams
- Reading: University of Hong Kong’s Critical Thinking Web: Joe Lau
and Jonathan Chan’s Venn Diagrams: “Tutorial V04”
Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and
Jonathan Chan’s Venn Diagrams: “Tutorial
V04” (HTML)
Instructions: Read this tutorial on notation with exist. Now that
you have the basic principles of using Venn diagrams in place, you
can use them to illustrate statements like “some A exists,”
“something exists that is an A,” or “something is A.”
Complete the exercises for the tutorial. Then, check your answers
against the “Tutorial V04 Answer
Key”
(PDF).
Reading this tutorial and completing the exercises should take
approximately 1 hour.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/).
5.1.4 Review of Introduction to Venn Diagrams
- Assessment: University of Hong Kong’s Critical Thinking Web: Joe
Lau and Jonathan Chan’s Venn Diagrams: “Exercises V01.6”
Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and
Jonathan Chan’s Venn Diagrams: “Exercises
V01.6”
(HTML)
Instructions: Complete these exercises relating to two-circle Venn
diagrams. For each question, you must choose the sentence that best
represents what is shown in the given diagram.
Completing this assessment should take approximately 30 minutes.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/venn/ex01.php).
5.2 Venn Diagrams and Arguments
5.2.1 Using Venn Diagrams to Evaluate Syllogisms
- Reading: University of Hong Kong’s Critical Thinking Web: Joe Lau
and Jonathan Chan’s Venn Diagrams: “Tutorial V06”
Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and
Jonathan Chan’s Venn Diagrams: “Tutorial
V06” (HTML)
Instructions: Read this tutorial on how to use Venn diagrams to
evaluate arguments. You will be introduced to the concept of a
syllogism, a special type of argument that cannot be evaluated in
SL. Venn diagrams are ideal for evaluating this type of argument.
Remember that a Venn diagram can only tell us if an argument is
valid, not whether it is sound.
Reading this tutorial should take approximately 30 minutes.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/).
5.2.2 Understanding the Logic of Venn Diagrams
- Reading: Butte College: Wu Wei-Ming’s iLogic: “Chapter 2,
Section 5: Venn Diagrams”
Link: Butte College: Wu Wei-Ming’s iLogic: “Chapter 2, Section 5:
Venn
Diagrams” (HTML)
Instructions: Read section 5 of chapter 2. The content reviews how
to set up Venn diagrams as well as the rules for using Venn diagrams
in evaluating argument validity. It also introduces the notion of
conditional validity and explains how to use Venn diagrams to
evaluate the validity of categorical syllogisms. Complete the
exercises using the interactive features on the page in order to
test your understanding.
Reading this section should take approximately 1 hour and 30
minutes.
Terms of Use: This resource is licensed under a Creative Commons
Attribution-NonCommercial-NoDerivs 3.0 Unported
License. It is
attributed to Wu Wei-Ming, and the original version can be found
here.
5.2.3 The Limitations of Venn Diagrams
- Reading: University of Hong Kong’s Critical Thinking Web: Joe Lau
and Jonathan Chan’s Venn Diagrams: “Tutorial V08”
Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and
Jonathan Chan’s Venn Diagrams: “Tutorial
V08” (HTML)
Instructions: Read this tutorial about the limitations of Venn
diagrams. Although Venn diagrams are a powerful tool for
representing some types of statements, there are many statements
that they cannot handle.
Complete the exercises for this tutorial. Then, check your answers
against the “Tutorial V08 Answer
Key”
(PDF).
Reading this tutorial and completing the exercises should take
approximately 30 minutes.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/).
5.2.4 Review of Venn Diagrams and Arguments - Assessment: University of Hong Kong’s Critical Thinking Web: Joe Lau and Jonathan Chan’s Venn Diagrams: “Tutorial V07” Link: University of Hong Kong’s Critical Thinking Web: Joe Lau and Jonathan Chan’s Venn Diagrams: “Tutorial V07” (HTML)
Instructions: Complete these exercises in which case you will
determine whether these arguments are valid or not. Draw out the
Venn diagrams with pencil and paper. If you use the HTML version,
note that you can click on the refresh button on your web browser to
generate a new set of questions.
Completing this assessment should take approximately 30 minutes.
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-Non-Commercial-Share-Alike License
3.0](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Joe Lau and Jonathan Chan, and the original version
can be found [here](http://philosophy.hku.hk/think/).
- Activity: The Saylor Foundation’s “PHIL102 Discussion Forum”
Link: The Saylor Foundation’s “PHIL102 Discussion
Forum”
(HTML)
Instructions: Consider how you might adapt Venn diagrams to evaluate the validity of the following arguments. Share your thoughts on the discussion forum by clicking on the link above and creating a free account, if you have not already done so. Review and respond to at least one or two other students’ posts.
1. Most cooks are men. Most men are idiots. So most cooks are idiots.
2. Very few plants are purple. Very few purple things are edible. So very few plants are edible.
Completing this activity should take approximately 30 minutes.
Terms of Use: The questions presented above are adapted from the University of Hong Kong’s Critical Thinking Web, which is licensed under a Creative Commons Attribution-Non-Commercial-Share-Alike License 3.0. It is attributed to Joe Lau and Jonathan Chan, and the original version can be found here.