a) Start with a Venn Diagram and label the
different categories:
b) Fill in the number of students who own both
cars and stereos, which would be in the
intersection of the two sets:

c) Fill in the remaining numbers for the two
sets. In this case, since a total of 45 students
own cars, and 35 have already been listed, then 45
- 35 = **10** students own cars only. Similarly,
since 75 students own stereos and 35 have already
been listed, then 75 - 35 = **40** students who
own stereos only:

d) Finally, interpret and answer the
questions:

**How many
students owned either a car or a
stereo?**
The question asks **either ... or** which
is **union of the sets**.

From the diagram, the number of elements in A =
10 + 35

and the number of elements in B which are
**NOT** in A are 40.

So the union would be 10+35+40 = **85**

How many students did
not own either a car or a stereo?

The question asks for the number not in
either A nor B

(namely, the complement of A
B or (A B)'
).

Since there are 100 students in the universe,
then the complement is found

by subtracting those who own either a car or
stereo from the total number of students
surveyed

or 100 - 85 = **15.**