Foundations 120
Section 3.1
Set: a collection of distinct objects. For example,

{1,2,3,4,5,6} is the set of Natural numbers less than 7.
Element: each object in a set. For example, 4 is an element of N, the set of Natural numbers.
Universal Set: a set of all the elements under consideration for a particular context. For example:
S

{Amber, Ben, Collin, Courtney, Garrett,..., Yihui, Yu Qing} is the universal set of all the students in Ms. Sewell’s
Foundation 12 class this semester.
Subset: a set whose elements all belong to another set. For example, F

{Ben, Victoria, Rebecca, Taylor, Jenna, Spencer} , the students in the front row is a subset of all the students in Ms.Sewell’s Foundation 12 class this semester. In set notation, this relationship is written F

S
Complement: all the elements of a universal set that do not belong to a subset of it. For example,
F ' {Max, Iftih, Collin, Jillian, Yihui, Natasha, Jiaqi, ..., Tristen, Rachel} are all the students in Ms. Sewell’s Foundation
Empty Set: a set with no elements. For example, the set of odd numbers divisible by 2, O

{ } or O
  is an empty set as well as a subset of the odd numbers. The set of Natural numbers less than 1, I

{ } or I
 
is also an example of an empty set. I

{ } or I
 
as well as a subset of the Natural numbers. You can think of an empty set as a box with nothing in it. The empty set is a subset of every set.
Disjoint: Two or more sets having no elements in common. For example, the set of even numbers and the set of odd numbers, the students in Ms. Sewell’s Foundation class and the students in Mr. Batt’s Foundation classes.
Jillian is studying the provinces and territories of
Canada. How can she use sets to categorize
Canada’s regions?
1.
List the elements of the universal set of
Canadian provinces and territories, C.

Foundations 120 Section 3.1
2.
One subset of C is the set of Western provinces and territories, W. Write W in set notation.
3.
The Venn diagram represents the universal set, C. The circle in the Venn diagram represents the subset W. The complement of
W is W’. a.
What does W’ contain? b.
Write W’ in set notation. c.
Explain what W’ represents in the Venn diagram. d.
Jillian wrote the set of Eastern provinces as

{ , , , , , } . Is E equal to W’? e.
List T, the set of territories in Canada. Is T a subset of C? Is it a subset of W, or a subset of W’. Explain. f.
List B, the set of provinces east of Newfoundland. g.
Consider sets C, W, W’, and T. List a pair of disjoint sets. Is there more than one pair of disjoint sets? h.
Draw a Venn diagram illustrating sets C, W, W’ and T.

Foundations 120
Section 3.1 a.
Indicate the multiples of 4 and 12, from 1 to 240 inclusive, using set notation. List any subsets. b.
Represent the sets and subsets in a Venn diagram.
Triangular numbers, such as
1, 3, 6, 10, or 15 can be represented as a triangular array. a.
Determine a pattern you can use to determine any triangular number.

Foundations 120 b.
Determine how many natural numbers from 1 to 100 are i.
even and triangular
First define the sets: U = {natural numbers from 1 to 100}
T = { triangular numbers from 1 to 100}
E = {even triangular numbers from 1 to 100}
Section 3.1 ii.
odd and triangular iii.
not triangular c.
How many numbers are triangular?
Infinite Set: a set with an infinite number of elements. The set of natural numbers would be an example of an infinite set.
Finite Set: a set with a countable number of elements. For example the set of natural numbers less than 7 is finite.

Foundations 120
Section 3.1
The Toronto Zoo is currently featuring polar bears, western grey kangaroos, cheetahs, African lions, white pelicans, snowy owls, northern bald eagles,
American alligators, and a boa constrictors. a.
Design a way to organize the animals for the zoo website. Represent your organization using a Venn diagram. b.
Name any disjoint sets. c.
Show which sets are subsets of one another using set notation.

Foundations 120
Section 3.1
The possible sums that can occur when you roll two six-sided dice are recorded in the outcome table to the right. a.
Display the following sets in one Venn diagram: i.
Rolls that produce a sum less than six ii.
Rolls that produce a sum greater than six. b.
Record the number of elements in each set. c.
Determine a formula for the number of ways that a sum less than or greater than six can occur. Verify your formula.
Mutually Exclusive: two or more events that cannot occur at the same time. For example:

When you toss a die once, it can be 1 or 2 or 3 or 4 or 5 or 6 but not all of them.

Leaving the FHS parking lot after school, you can turn left or right but not both.

Foundations 120 Section 3.1