Sec. 2.5 Applications of Sets

1
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
Check the appropriate box or boxes
1. I enjoy cross- country skiing 2. I enj
oy downhill skiing
2
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
Check the appropriate box or boxes
1. I enjoy cross- country skiing 2. I enj
oy downhill skiing
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
3
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
4
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





20
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
5
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





60
20
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
6
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
7
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
8
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
30
9
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
30
60
10
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
30
60
50
11
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
30
60
50
20
12
Sec. 2.5 Applications of Sets
At the ABC Sports Shop, 160 people were
selected at random and asked to complete th
e questionnaire below
It was found that 80 people checked box 1,
indicating that they enjoy cross-country skiing,
70 people checked box 2, and 20 checked both
boxes, indicating that they enjoy both
cross-country and downhill skiing.
U enjoy
enjoy cross-country
downhill skiing
skiing





50
60
20
30
a. How many people did not check a box?
b. How many people enjoy cross-country skiing
but do not enjoy downhill skiing?
c. How many people enjoy downhill skiing but do
not enjoy cross-country skiing?
How many people enjoy downhill and cross-country
skiing? How many people enjoy downhill or cross-c
ountry skiing?
30
60
50
20
130
13
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
14
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
3
15
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
3
2
16
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
3
5
2
17
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
8
3
5
2
18
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
8
3
5
2
4
19
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
8
6
3
5
2
4
20
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
U Set Chemistry
Theory


Psycho
logy
8
6
2
3
5
2
4
21
Sec. 2.5 Applications of Sets
2. In a group of students 15 are studying Set
Theory, 22 are studying Chemistry, 14 are
studying Psychology, 11 are studying both Set
Theory and Chemistry, 8 are studying Chemistry
and Psychology, 5 are studying Set Theory and
Psychology, and 3 are studying all three
subjects. How many are studying only Set Theory?
2
U Set Chemistry
Theory


Psycho
logy
8
6
2
3
5
2
4
22
Sec. 2.5 Applications of Sets
3. Molly was hired to interview people to find
out what brand of ice cream they liked. She
submitted the following report.
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen Custar
d 61 Number of people who liked bo
th Carvel and Abbott's Frozen Custard
40 Every person interviewed liked one or
the other or both flavors of ice cream. When
Molly turned in her report, she was fired. Why?
23
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





24
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





40
25
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





38
40
26
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





21
38
40
27
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





21
38
40
1
28
Sec. 2.5 Applications of Sets
Number of people interviewed 100
Number of people who liked Carvel 78
Number of people who liked Abbott's Frozen
Custard 61
Number of people who liked both Carvel
and Abbott's Frozen Custard 40
Every person interviewed liked one or the other
or both flavors of ice cream. When Molly turned
in her report, she was fired. Why?
U Like
Like Carvel
Abbotts
Frozen Custard





21
38
40
1