Venn Diagrams
Name__________________________
Answer the following based on sample space using a Venn Diagram.
1. Use the sets below to answer parts (a) through (f):
U = {1, 2, 3, 4, 5, 6, 7, 8, 9. 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A = the numbers in U that divide 12 with no remainder
B = the numbers in U that divide 15 with no remainder
C = the numbers in U that divide 20 with no remainder
a. A  B
d. A  B
b. B  C
e. A  C
c. A  B  C
f. A   B  C 
2. Make and label a Venn diagram for the following data where A, B, and C are subsets of
the universe of people who were surveyed about the type of meat they like to eat. Let
A represent the people who like steak, B is the set who like chicken, and C is the set
who like pork.
n(U) = 350
n(A) = 150
n( B) = 195
n( C) = 170
n(A  B) = 99
n(B  C) = 103
n(A  C) = 62
n(A  B  C) = 56
Given the following Venn Diagram, answer #3.
3. Find the following
a. A   B  C   _______________
b. B  A  _______________
c.

A
B
c
a,b
h
d

B  C  A  _______________
f,g
e
i, j
d. C  _______________
C
4. Shade the following on the Venn Diagrams below.
a. A  B
b.  A  B   C
A
A
B
B
C
C
Given the following Venn Diagram, answer #1.
5. Find the following
a. A  B  _______________
A
b.
 B  C   A  _______________
c.
A  B  C  _______________
d.
C  _______________
e.
A  B = ________________
c
a,b
h
d
f,g
e
i, j
C
6. Shade the following on the Venn Diagrams below.
a. A  B
b.
A
B
 A  B C
A
B
B
C
C
7. Make and label a Venn diagram for the following data where A, B, and C are subsets of the universe of
people who were surveyed about the type of food they like to eat. Let A represent the people who like
hamburgers, B is the set who like hot dogs, and C is the set who like pizza.
n(U) = 400
n(A) = 150
n( B) = 140
n( C) = 120
n(A  B) = 70
n(B  C) = 90
n(A  C) = 50
n(A  B  C) = 30
U = {a, b, c, d, e, f, g, h}
8. Create a venn diagram and then answer the questions.
a. A  B
e. A  C
b. B C
f. A  B  C
c. A  B
g. B  C
d.
 AC  B
h. B  C
A = {a, c, e}
B = {b, c, d}
C = {c, e, h}