Math 30-2
Set Theory & Probability: Lesson #1
Introduction to Sets
Objective: By the end of this lesson, you should be able to:
- provide examples of the empty set, disjoint sets, subsets, and the universal set in a given context.
- use set notation, including the symbols , and Ø
- determine the elements in the complement of a set.
- organize set information using a Venn diagram.
A set is
Sets can be numerical; for example, the set of whole numbers:
But sets can also include non-mathematical elements, such as species of animals, items of clothing, types of food, residents of Hinton, models of cars, etc.
In order to explore vocabulary related to sets, let’s consider the set of Canadian provinces and territories, which we will call C. (See p. 6 of your textbook if you need a map of Canada to help you.)
Vocabulary:
· Element –
e.g. 1) Give an example of one element in the set of Canadian provinces and territories, C.
· Universal set –
e.g. 2) List the universal set of C.
· Subset –
e.g. 3) One subset of C is the Maritime provinces, M. Write M in set notation.
In set notation, the relationship between a set and a subset is written as:
· Complement –
The complement of a subset is denoted by ______.
e.g. 4) The set of Western provinces is W = {BC, AB, SK, MN}. Is ? Explain. If not, describe in words and list the elements in .
· Empty set –
The empty set is denoted by the symbol ______or ______.
e.g. 5) Explain why you can represent the set of Canadian provinces in the southern hemisphere, S, by the empty set.
· Disjoint sets –
e.g. 6) Describe a subset of C that is disjoint with W.
· Finite set –
In set notation, the number of elements in a set X is denoted ______.
e.g. 7) Determine .
· Infinite set –
e.g. 8) Give an example of an infinite set.
Graphic organizers, such as Venn diagrams, can be used to illustrate the relationships between subsets.
e.g. 9) Consider the following subsets of C:
W: Western provinces M: Maritime provinces
E: Eastern provinces T: Territories
a) Draw a Venn diagram that shows the relationships between these subsets of C.
b) Name two pairs of disjoint sets.
c) Show which sets are subsets of one another using set notation.
d) Explain what is meant by the statement . Is this statement true or false?
e) Find and .
f) If , make a generalization about and .
g) Describe . Which subsets of C are also subsets of ?
h) Find and . Make a generalization about the sum of the number of elements in a subset and its complement.
Assignment: p. 14-17 #1-2, 4a-d, 5-6, 8-11, 16