A pet store surveyed people to see how many own a cat and how many own a dog. The Venn diagram below shows the results. (Each number gives the number of people who fall into that Venn diagram category.) (a)How many of the people own a dog? (b)How many of the people own a cat or a dog (or both)? (c)How many of the people do not own both a cat and a dog?

(a) The number of people who own a dog is the sum of the number of people in the "Dog" circle and the number of people in the overlapping region (since they own both a cat and a dog).

(b) The number of people who own a cat or a dog (or both) is the sum of the number of people in the "Cat" circle, the number of people in the "Dog" circle, and the number of people in the overlapping region.

(c) The number of people who do not own both a cat and a dog is the sum of the number of people in the "Cat" circle and the number of people in the "Dog" circle.

Let's denote:

�

C as the number of people who own a cat

�

D as the number of people who own a dog

�

CD as the number of people who own both a cat and a dog

Given:

�

=

15

C=15

�

=

20

D=20

�

=

10

CD=10

(a) Number of people who own a dog:

�

+

�

=

20

+

10

=

30

D+CD=20+10=30

(b) Number of people who own a cat or a dog (or both):

�

+

�

+

�

=

15

+

20

+

10

=

45

C+D+CD=15+20+10=45

(c) Number of people who do not own both a cat and a dog:

�

+

�

=

15

+

20

=

35

C+D=15+20=35