This document explains Venn diagrams and how to use them to represent relationships between different sets of data. It defines universal sets, subsets, disjoint sets, intersections, and complements. It then provides an example of using a Venn diagram to represent the results of a survey where the universal set is 100 people and the sets are cat owners, dog owners, and those who own neither. The Venn diagram shows the numbers that fall into each category and their intersections to calculate how many owners have both a dog and a cat.

2. These sets can be visualized with circles in what is called a Venn Diagram.
A B
A B
Everything that is in A or B.
A B
A B
Everything that is in A AND
B.
A B

3. Often will have a set that contains all elements that we wish to consider. This
is called the universal set. All other sets are subsets of this set.
Universal Set
A B
A B =
There are no
elements in
both A and B.
When this is
the case they
are called
disjoint sets.
A
This means the complement of A, and means the set
of all elements in the universal set that are not in A.
A A

4. 100 people were surveyed. 52 people in a survey owned a cat. 36 people
owned a dog. 24 did not own a dog or cat.
Draw a Venn diagram.
universal set is 100 people surveyed
C D
Set C is the cat owners and Set D is the dog owners. The
sets are NOT disjoint. Some people could own both a dog
and a cat.
24
Since 24
did not own
a dog or
cat, there
must be 76
that do.
n(C D) = 76
This n means the
number of elements
in the set
52 + 36 = 88 so
there must be
88 - 76 = 12
people that own
both a dog and
a cat.
12
40 24
Counting Formula:
n(A B) = n(A) + n(B) - n(A B)

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