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© 2014 Pacific Crest
61
2.1
Basics of Set Theory
P
urpose
The role this topic plays in quantitative reasoning
Set theory
is the process of organizing objects by their defined characteristics. By defining characteristics
of sets, we use set operations to analyze the relationship between sets. The idea of being able to classify
and organize data into sets and then work with these sets extends into many areas of quantitative reasoning.
In this book alone, we use set-based quantitative thinking in at least 20 other experiences the following
chapters: Probability, Mathematical problem solving, Making data valuable, Graphics, Data and statistical
analysis, Financial analysis, and Mathematical modeling.
L
earning Goals
What you should learn while completing this activity
1. Understand the characteristics of objects and sets in order to make effective decisions.
2. Characterize an object with important labels and identifiers (meta-data).
3. Use standard set operators (union, intersection, and complement) and tools like Venn diagrams on various
types of sets including universal sets, subsets, and proper subsets.
4. Expand the use of set theory within your quantitative reasoning tool set.
D
iscovery
Finding out for yourself
There are many ways in which we can use sets to organize our thinking, resources, and information.
Select one of the following three exercises to complete and think about.
1. Consider the organization of your contacts on your email program, your cell phone, or the social
media you use (things like Facebook
or
LinkedIn). Consider the organization of files and file folders,
or your digital images on your computer. Consider the organization of an investment portfolio into
stock, commodity, or bond groups. Of all the different characteristics that each of these set objects
has, which are the most critical (i.e., which characteristics allow you to find, combine,or separate
specific objects)? How would you organize those characteristics into specific sets?
2. Suppose you were going to plan a big event like a charity fund raiser or wedding. How would you
organize your various contacts into logical sets? Play with the number of possible sets A) before
sending out invitation and B) as you receive RSVPs.
3. How have you organized your file system on your computer? How many sets do you have? Is a
folder a set and is a folder within a folder a subset? What is the largest set? The smallest? Is there
anything that is not part of a set?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. Other than the examples given of contacts, file folders, or investment portfolios, what other examples
of sets do you see and use in your daily life?
2. Consider how one of your contacts can be in more than one set, for example a relative and a neighbor.
Can you give another example?