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14-1 Sets
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
14-1 Sets
Warm Up
Fill in each blank.
1. A ________ is a number that can be
n
expressed in the form d , where n and d are
integers and d ≠ 0. rational number
2. The set of _________ consists of the set
of rational numbers and the set of irrational
numbers. real numbers
3. The set of _________ consists of the set
of counting numbers, their opposites, and
zero. integers
Pre-Algebra
14-1 Sets
Problem of the Day
Use a traditional clock face to determine
the next three terms in the following
sequence: 1, 6, 11, 4, 9, . . .
2, 7, 12
Pre-Algebra
14-1 Sets
Learn to understand mathematical sets
and set notation.
Pre-Algebra
14-1 Sets
Insert Lesson Title Here
Vocabulary
set
element
subset
finite set
infinite set
Pre-Algebra
14-1 Sets
A set is a collection of objects, called
elements. Elements of a set can be
defined in two ways: roster notation
and set-builder notation.
Pre-Algebra
14-1 Sets
Set
Even
counting
numbers
Roster Notation Set-Builder Notation
{2, 4, 6, 8,
10, …}
{x|x is an even counting
number}
Read as “the set of all x
such that x is an even
counting number.”
{Huron, Ontario, {x|x is one of the
Great Lakes Michigan, Erie,
Great Lakes}
Superior}
Pre-Algebra
14-1 Sets
The symbol  is read as “is an element of.” Read
the statement 3  {odd numbers} as “3 is an
element of the set of odd numbers.” The symbol
 is read as “is not an element of.” Read the
statement 2 {odd numbers} as “2 is not an
element of the set of odd numbers.”
Helpful Hint
Think of the element symbol  as the letter e.
Pre-Algebra
14-1 Sets
Additional Example 1: Identifying Elements of a Set
Insert  or  to make each statement true.
A. 4
{even integers}
4  {even integers}
B. shoes
4 is an even integer.
{furniture}
shoes  {furniture}
Shoes are not furniture.
C. rhombus
{quadrilaterals}
A rhombus is a
rhombus  {quadrilaterals}
quadrilateral.
Pre-Algebra
14-1 Insert
Sets Lesson Title Here
Try This: Example 1
Insert  or  to make each statement true.
A. 3
{odd integers}
3  {odd integers}
B. shirts
{coats}
shirts  {coats}
C. square
{rectangles}
square  {rectangles}
Pre-Algebra
3 is an odd integer.
Shirts are not
coats.
A square is a
rectangle.
14-1 Sets
Set A is a subset of set B if every element
in A is also in B. The symbol  is read as
“is a subset of” and the symbol  is read
as “is not a subset of.”
Pre-Algebra
14-1 Sets
Additional Example 2: Identifying Subsets
Determine whether the first set is a subset of
the second set. Use the correct symbol.
A. E = {even numbers} Q = {rational numbers}
Every even number is a
Yes, E  Q.
rational number.
B. A = {1, 2, 3, 4}
B = {3,4}
No, A  B.
C. C = {squares}
Yes, C  D.
Pre-Algebra
1 and 2 are not in the
second set.
D = {rectangles}
All squares are rectangles.
14-1 Insert
Sets Lesson Title Here
Try This: Example 2
Determine whether the first set is a subset of
the second set. Use the correct symbol.
A. R = {sandals}
Yes, R  S.
B. B = {1, 2, 5, 7}
No, B  C.
C. E = {circles}
Yes, E  F.
Pre-Algebra
S = {shoes}
Sandals are a type of shoe.
C = {1, 2, 5, 8}
7 is not in the second set.
F = {ovals}
A circle is not an oval.
14-1 Sets
A finite set contains a finite number of
elements. An infinite set contains an
infinite number of elements.
Pre-Algebra
14-1 Sets
Additional Example 3: Identifying Finite and Infinite
Sets
Tell whether each set is finite or infinite.
A. {students in a school}
finite
There are a specific number
of students in a school.
B. {points on a line segment}
infinite
Between any two points there
is always another point.
C. {multiples of 5}
infinite
Pre-Algebra
Any number can be multiplied
by 5.
14-1 Insert
Sets Lesson Title Here
Try This: Example 3
Tell whether each set is finite or infinite.
A. {hairs on your head}
finite
There are a specific number
of hairs on a person’s head.
B. {whole numbers between 1 and 10}
finite
There are exactly 8 numbers
in the set.
C. {real numbers between 1 and 10}
infinite
There are an infinite number of real
numbers between any two numbers.
Pre-Algebra
14-1 Sets
Insert Lesson Title Here
Lesson Quiz: Part 1
Insert  or  to make each statement true.
{whole numbers} 
1. 0
2. – 1
2
{integers}

Determine whether the first set is a subset of
the second set. Use the correct symbol.
3. T = {counting numbers}
No; T  P
P = {prime numbers}
4. A = {a, e, o}
Z = {vowels}
Pre-Algebra
Yes; A  Z
14-1 Sets
Insert Lesson Title Here
Lesson Quiz: Part 2
Tell whether each set is finite or infinite.
5. {two-digit whole numbers} finite
6. {polygons}
Pre-Algebra
infinite