### 3-8 Unions and Intersection of Sets

```3-8
Unions and
Intersection of Sets
The Union of two or more sets is the
set that contains all elements of the
sets
Symbol: ∪
How to find: list the elements that are
in either set, or in both sets
Problem 1: Union of Sets
In your left pocket, you have a quarter, a
paper clip, and a key. In your right pocket,
you have a penny, a quarter, a pencil, and a
marble. What is a set that represents the
P={0, 1, 2, 3, 4}
Q={2, 4}
What is  ∪
The Intersection of two or more sets is
the set of elements that are common
to every set
Symbol: ∩
How to Find: list only the elements
that are in both sets
Disjoint sets have no elements in
common
The intersection of disjoint sets is the
empty set
Problem 2: Intersection of Sets
X={x|x is a natural number less than 19}
Y={y|y is an odd integer}
Z={z|z is a multiple of 6}
What is  ∩ ?
X={x|x is a natural number less than 19}
Y={y|y is an odd integer}
Z={z|z is a multiple of 6}
What is Y ∩ ?
Problem 3: Making a Venn Diagram
A={x|x is one of the first five letters in the
English alphabet}
B={x|x is a vowel}
C={x|x is a letter in the word VEGETABLE}
Which letters are in all three sets (Draw a
Venn Diagram)?
Problem 4: Using a Venn Diagram to Show
Numbers of Elements
Of 500 Commuters polled, some drive
to work, some take public
transportation, and some do both.
Two hundred commuters drive to work
and 125 use both types of
transportation. How many commuters
take public transportation?
```