Algebra 1 Common Core Student Edition, Grade 8-9

Working With Sets

Common Core State Standards

A -R E I.B .3 Solve linear equations and inequalities

in one variable, including equations w ith coefficients

represented by letters.

MP 1, MP 2, MP 6

Ob ject ives To write sets an d identify subsets

To find th e co m p lem en t of a set

Getting Ready! X C

How can you

organize the

choice of letters

to help you solve

this problem?

Most numbers on a telephone keypad correspond to a

set o f l et t er s. Suppose you' re sending a t ex t m essage.

You p r ess 4 , 6 , 6 , and 3 , in t h a t o r d er —one num ber

for each letter. What word might your telephone think

yo u' re t r y i n g t o sp el l? W h at w o r d s could you b e t r y i n g t o

sp el l? Ex p l ain yo u r r easo n i n g.

(^1) ABC (^2) DEF 3
GHI^4 JKL^5 MNO^6
PQRS^7
00 1
WXYZ^9
*^0 #
MATHEMATICAL
PRA CTICES
Lesso n
Vocabulary
roster form

• set-builder
  notation
  •em pty set


• universal set


• complement of
  a set

A

Recall from Lesson 1-3 th at a set is a collection of distinct elem ents. A subset c o n t a i n s

elem ents from a set. For example, th e n u m b e r 6 on th e telep h o n e keypad corresponds

to th e set {M, N, O}. The set {M, 0 } is one subset of this set.

Essent ial Und er st and ing Sets are th e basis of m athem atical language. You can

w rite sets in different ways an d form sm aller sets of elem ents from a larger set. You can

also describe th e elem ents th a t are not in a given set.

Roster form is one way to write sets. Roster form lists the elem ents of a set within

braces, { }. For example, you write the set containing 1 and 2 as {1, 2}, and you write the

set of multiples of 2 as { 2, 4,6,8,...}.

Set-builder notation is a n o th e r way to write sets. It d escribes th e properties an elem ent

m ust have to be inclu d ed in a set. For example, you can w rite th e set { 2 ,4 ,6, 8,...}

in set-builder n o tatio n as {x | x is a m ultiple of 2}. You read this as “th e set of all real

n u m b ers x, such th a t x is a m ultiple of 2 .”

Plan fJ Problem 1 Using Roster Form and Set-Builder Notation

How are roster form

and set-builder

notation different?

Roster form lists the

elements of a set.

Set-builder notation

describes the properties

o f those elements.

How do you write "7 'is the set of natural numbers that are less than 6 ” in roster

form? In set-builder notation?

Ro st er f o r m Set - b u i l d er n o t at i o n

Write "T is

as "T = ."

List all natural numbers

th a t are less than 6.

T = {1, 2, 3, 4, 5}

Use a variable.

V"

T = {x | x is a n atural num ber, x < 6 }

Describe the lim its on

the variable.

v—y— -----------

194 Chapter 3 Solving Inequalities