MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
Shade the Venn diagram to represent the set
A' U (A ∩ B)
A
U
B
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
What regions make up X ∩ W' ∩ Y ?
U
W
𝑟3
𝑟2
𝑟5
𝑟1
X
𝑟6
𝑟8
𝑟4
𝑟7
Y
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
Use the given information to fill in the number of elements
for each region in the Venn diagram below.
n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38
A
U
B
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
Find the number of elements in each region below.
n(A∩B∩C)=2
n(C)=29
n(A∩C)=10 n(A∩C')=28
n(A'∩B'∩C')=8
n(A∩B)=9
n(B∩C)=11
n(B')=41
B
A
U
C
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
Find the number of elements in sets A, B & C if:
A∩B=Ø
n(B∩C)=3
n(A ─ C)=1
n(U)=19
n(A∩C)=11
n(C ─ A)=7
n(B∩C)=11
B
A
U
C
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
The number of animals counted in wildlife observations of a
certain watering hole are shown by class and time of highest
activity (see table). Using the letters in the table, find
n(A ∪ D) and n(B ⋂ F).
Mammals
Birds
Reptiles Fish
Morning
(E)
Afternoon
(F)
Evening
(G)
Total
(A)
(B)
(C)
(D)
Total
111
54
6
80
251
31
9
1
29
70
10
3
48
24
85
152
66
55
133
406
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
Fill in the number of elements
A
in each region.
U
C
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
How many had only volleyball?
A
6
6
4
5
U
7
6
1
C
57
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
How many had soccer & rugby
A
6
6
but not volleyball?
4
5
U
7
6
1
C
57
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
How many had soccer or rugby?
A
6
6
4
5
U
7
6
1
C
57
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
How many had soccer or rugby
A
6
6
but not volleyball?
4
5
U
7
6
1
C
57
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
92 cities were surveyed to determine sports teams.
24 had soccer
13 had soccer & rugby
7 had all three
23 had rugby
12 had soccer & volleyball
19 had volleyball 13 had rugby & volleyball
B
How many had exactly 2 teams?
A
6
6
4
5
U
7
6
1
C
57
MATH 110 Sec 2-4: More Venn Diagrams
Practice Exercises
A survey of 260 families:
99 had a dog
98 had neither a dog nor a cat
76 had a cat
and also had no parakeet
34 had a dog & cat 8 had a dog, a cat & a parakeet
How many had a parakeet only?
B
A
U
C