Algebra 1 Common Core Student Edition, Grade 8-9

W hen w orking w ith sets, you call th e largest set you are using the universal set, or

universe. The com plem ent of a set is th e set of all elem ents in th e universal set th at are

n ot in th e set. You d enote the co m p lem en t of A by A '.

In th e Venn diagram s below, U represents the universal set. Notice th a t AC U

and A' C U.

Set A is s h a d e d. T h e c o m p le m e n t o f s e t A is s h a d e d.

Problem 4 Finding the Com plem ent of a Set

Universal set U = {king, queen, bishop, knight, rook, pawn} and set A is the set of

chess pieces that move side to side. What is the complement of set A?

Know

• The elements of set U


• The elements of set A

iN e e d

• The elements
  of A'

Plan

Use a V enn d ia g ra m to fin d a ll th e

elements in set U that are not in set A.

The Venn diagram shows the

relationship between sets A and U. The

elem ents in set U th at are not in set A

are bishop, knight, a n d pawn.

So, A' = {bishop, knight, pawn}.

G o t It? 4. Universal set U = {months of the year} and

set A = { m onths w ith exactly 31 d ay s}. W hat is th e co m p lem en t of set A?

Write your answ er in roster form.

Complement

of Set A

196 Ch ap t er 3 So l v i n g I n e q u a l i t i e s