Question

7 of the people in Aubrey's office like to eat cheeseburgers. 4 people like to eat cookies, and 3 people like to eat both cheeseburgers and cookies. How many people like to eat cookies but not cheeseburgers?

Hint: Copy and complete the Venn diagram below to help you solve the problem.

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I like to eat cheeseburgers
I like to eat cookies

people

Answer 1

To solve the problem using a Venn diagram, let's first define the data we have:

- Let \( A \) be the set of people who like cheeseburgers.
- Let \( B \) be the set of people who like cookies.

From the problem:
- \( |A| = 7 \) (people who like cheeseburgers)
- \( |B| = 4 \) (people who like cookies)
- \( |A \cap B| = 3 \) (people who like both cheeseburgers and cookies)

We want to find the number of people who like cookies but not cheeseburgers, which is represented by \( |B - A| \).

To find this, we can use the formula:

\[
|B - A| = |B| - |A \cap B|
\]

Substituting in the numbers we have:

\[
|B - A| = 4 - 3 = 1
\]

So, **1 person likes to eat cookies but not cheeseburgers**.

### Summary:
- People who like only cheeseburgers: \( |A| - |A \cap B| = 7 - 3 = 4 \)
- People who like only cookies: \( |B| - |A \cap B| = 4 - 3 = 1 \)
- People who like both: \( |A \cap B| = 3 \)

If we complete the Venn diagram, it can look like this:

- In the cheeseburger section (only cheeseburgers): 4 people
- In the cookie section (only cookies): 1 person
- In the overlapping section (both): 3 people