Algebra 1 Common Core Student Edition, Grade 8-9

Why are sets Y and 1
disjoint?
Every element of Z is a
multiple of 6, so every
element o fZ is even.
Y contains only odd
numbers. So no element
of Z belongs to Y.

How do you know
where in the diagram
to place each item?
Items that the friends
have in common belong
in an intersection. Use
the Venn diagram to
determine the correct
intersection.

Intersection of Sets

Set X = (x | x is a n a t u r a l n u m b e r le s s t h a n 1 9 } , s e t Y = {y \ y is a n o d d i n t e g e r } ,

and set Z = {z \ z is a m u l t i p l e o f 6 }.

Q W h a t is X D Z?

List the elements that are both natural num bers less than 19 and m ultiples of 6:

xnz={6, 12 , 18 }.

0 What is fflZ?

L is t t h e e le m e n ts t h a t a re b o t h o d d in te g e r s a n d m u lt ip le s o f 6. T h e re a re n o

multiples of 6 that are also odd, so Y a n d Z a re d i s jo in t sets. T h e y h a v e n o e le m e n ts i n

com m on. YD Z = 0, th e e m p ty set.

^ Got It? 2. Let A = {2, 4, 6, 8}, B = {o, 2, 5 ,7 , 8 }, a n d

C = { n | n is a n o d d w h o le n u m b e r }.

a. What is 4(1 B? b. What is A H C? c. What is C D £?

You can draw Venn diagram s to solve problem s involving relationships between sets.

Making a Venn Diagram

Camping T h r e e f r i e n d s a r e g o in g c a m p in g. T h e it e m s i n e a c h o f t h e i r b a c k p a c k s

f o r m a s e t. W h i c h it e m s d o a l l t h r e e f r i e n d s h a v e i n c o m m o n?

W-Pr o b l em 3

D r a w a V e n n d ia g r a m to

represent the u n io n and

in te rs e c tio n o f th e sets.

A l l th r e e f r ie n d s h a v e a h a t, a m a p , a n d a b o t t le o f w a t e r i n t h e i r b a c k p a c k s.

blue bag

2 1 6 Chapter 3 Solving Inequalities