Venn Diagrams
Solve the problem by drawing a diagram and
using logical reasoning.
1. Eighteen students in a class play baseball.
Seventeen students in the class play basketball.
Thirty students in the class play either or both
sports. Draw a Venn diagram to show the number
of students who play basketball and baseball.
a.
b.
3. In a marketing survey involving 1,000 randomly
chosen people, it is found that 630 use brand P, 420
use brand Q, and 210 use both brands. How many
people in the survey use brand Q and not brand P?
a. 210 people
b. 420 people
c. 630 people
d. none of these
4. Mr. Green teaches band, choir, and math. This
year, he has 57 students that take at least one of his
classes. He teaches band to 25 students. There are
48 students who take either band or choir or both.
There are 9 students who take both math and choir
with Mr. Green.
a. Complete the Venn diagram below.
b. How many students take exactly 2 classes from
Mr.Green?
c.
d.
2. In a school of 464 students, 89 students are in the
band, 215 students are on sports teams, and 31
students participate in both activities. How many
students are involved in neither band nor sports?
a. 160 students
b. 191 students
c. 249 students
d. 433 students
5. Every student in your class participates in band or a
sport, and some students participate in both. There
are 8 students who are in the band but do not play a
sport, and 22 students participate in a sport, which
includes the 7 students who play a sport and are
also in band. Use a Venn diagram to find how
many students are in your class.
ID: A
Venn Diagrams
Answer Section
1. A
2. B
3. B
4.
a.
b. 17 students
5.
30 students
1