# Geometry- Venn Diagrams Examples Practice by undul855

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```									                                    Geometry- Venn Diagrams Examples & Practice 2009

PART I – SETTING UP A VENN DIAGRAM. Writing statements using If-Then form.
Directions: Draw and label a Venn Diagram to illustrate each statement.

Example 1
All dogs are animals. Since dogs are types of animals, dogs belong to a larger set or group called animals.
(If it is a dog, then it is an animal).

animals

dogs

1. All drummers are in the band.

2. Vertical angles are congruent.

3. If two angles form a linear pair, then they are adjacent.

Example 2
Some students ski and some snowboard, while some do both.

Ski
Snowboard

4. Some students prefer chocolate chip cookies and some prefer oatmeal raisin, while some like both.

5. In one extended study, some of the students play soccer and some students play basketball, while a few
of the students play both.

6. Some of the students in the sophomore class choose to take Spanish, some choose to take Latin, while
some choose to take both.

Venn Diagram Practice                                                                               Page 1
Geometry- Venn Diagrams Examples & Practice 2009

Example 3
All the seniors were asked what their favorite subject is out of Math, Art and PE. Some students could not
decide so they chose two of the three, and some students said they liked all three equally.

Art
Math

PE

7. A group of people were asked about where they have traveled. They had all been to Europe, Australia
or Africa. Some had been to two of the three continents and some had traveled to all three.

8. All the freshmen were asked whether they liked dramas, comedies or horror movies. Some of them
liked two kinds and some liked all three.

PART II SOLVE PROBLEMS USING VENN DIAGRAMS

Example
400 Deep Run students were surveyed to see if they were on a sports team or a member of Key Club. 235
are on a sports team and 181 are members of Key Club, while 62 are both on a sports team and members of
Key Club.

Sport          Key Club

62
173
119

46

How many students are either members of Key Club or on a sports team?

How many students are not involved in Key Club or on a sports team?
354 + X = 400
X = 46
So 46 of the 400 students surveyed were not members of Key Club or on a sports team.

1. 42 students are in a class. 13 have birds, 21 have dogs, while 7 have both birds and dogs. How many
students do not have a bird or a dog?
How many students have ONLY birds?

Venn Diagram Practice                                                                             Page 2
Geometry- Venn Diagrams Examples & Practice 2009

2. 50 students went to a Richmond Braves game. 30 of them got a hot dog, 25 got a pretzel and 5 got both.
How many students ONLY got a pretzel?
How many students got a pretzel or a hot dog?

3. 78 students were asked if they liked Lunch or PE. 60 said they liked lunch, 38 said they liked PE and 27
said they liked both lunch and PE.
How many ONLY like PE?
How many ONLY like lunch?

4. In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many
students in the class are not enrolled in either Chorus or Band?

5. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60
students participate in both activities. How many students are involved in either band or sports?

6. Thirty-six people were polled on telephone usage. One-third of the people polled owned cell phones.
One fourth of the people owned pagers. Five people owned both pagers and cell phones. The rest of the
people did not own either. How many people polled did not own a pager or a cell phone?

7. A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish.
Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of
pets, how many patrons have none of these pets?

8. A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take
French, 16 want to take Spanish, and 11 want to take Latin. Five say they want to take both French and
Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How
many students want French only?

Venn Diagram Practice                                                                                   Page 3

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